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Search results for: AMENABLE MARKOV SEMIGROUP
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A note on a Wiener-Wintner theorem for mean ergodic Markov amenable semigroups
PublicationWe prove a Wiener-Wintner ergodic type theorem for a Markov representation of a right amenable semitopological semigroup.
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Types of Markov Fields and Tilings
PublicationThe method of types is one of the most popular techniques in information theory and combinatorics. However, thus far the method has been mostly applied to one-dimensional Markov processes, and it has not been thoroughly studied for general Markov fields. Markov fields over a finite alphabet of size m ≥ 2 can be viewed as models for multi-dimensional systems with local interactions. The locality of these interactions is represented...
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COMPARATIVE ANALYSIS OF RESULTS OF APPLICATION OF MARKOV AND SEMI-MARKOV PROCESSES TO RELIABILITY MODELS OF MULTI-STATE TECHNICAL OBJECTS
PublicationDuring rational operation of technical objects and systems various operational decisions are made and decision-making process itself should be consisted in selecting that considered most favourable out of all possible to be taken. Choice of such decision is possible after taking into account many different information items but it never be completely correct without accounting for data and indices dealing with reliability. In...
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Markov Model of Disease Development and Recovery
PublicationMarkov models are commonly used to simulate diseases and allow modeling of multiple health states and outcomes. Starting with the well known Le Bras multistate model (cascading failure model) with time-independent transitions we will see how simple Markov mortality models may be pressed into the service of survival and event history analysis. We will focus on more complex models which will be able to take into account remission,...
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Average Redundancy of the Shannon Code for Markov Sources
PublicationIt is known that for memoryless sources, the average and maximal redundancy of fixed–to–variable length codes, such as the Shannon and Huffman codes, exhibit two modes of behavior for long blocks. It either converges to a limit or it has an oscillatory pattern, depending on the irrationality or rationality, respectively, of certain parameters that depend on the source. In this paper, we extend these findings, concerning the Shannon...
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Laplace domain BEM for anisotropic transient elastodynamics
PublicationIn this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained....
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The use of Markov chains in the social convergence analysis
PublicationThe main goal of this article is to analyze the social convergence process using Markov chains. In this research, term social convergence refers to the reduction of dispersion in the standard of living among countries. The use of Markov chains in the social convergence analysis allowed describing movements of observational units within the distribution and providing more details about the mechanism of the convergence process. A...
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Survival time prognosis under a Markov model of cancer development
PublicationIn this study we look at a breast cancer data set of women from Pomerania region collected in year 1987-1992 in the Medical University of Gdańsk. We analyze the clinical risk factors in conjunction with Markov model of cancer development. We evaluate Artificial Neural Network (ANN) survival time prediction via a simulation study.
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Usage of Memi-Markov Process in Operation Evaluation of Diesel Engine
PublicationIn paper, the proposition of quantitative evaluation of operation using semi-Markov processes theories has been presented. Basic assumptions, essential for creating mathematical model on example of diesel engine were shown. Special attention was given to practical aspects of using established mathematical model. Example of characteristic of analysed process - temporary distribution of probability was assigned.
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Application of semi-Markov processes for evaluation of diesel engines reliability with regards to diagnostics
PublicationThe paper presents semi-Markov models of technical state transitions for diesel engines, useful for determination of their reliability, as a result of the conducted statistical empirical studies. Interpretation of technical states provided for this sort of engines refers to ship main engines, i.e. engines employed in propulsion systems of sea-going ships. The considerations recognize diesel engine as a diagnosed system (SDN), of...
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Hybrid of Neural Networks and Hidden Markov Models as a modern approach to speech recognition systems
PublicationThe aim of this paper is to present a hybrid algorithm that combines the advantages ofartificial neural networks and hidden Markov models in speech recognition for control purpos-es. The scope of the paper includes review of currently used solutions, description and analysis of implementation of selected artificial neural network (NN) structures and hidden Markov mod-els (HMM). The main part of the paper consists of a description...
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USEFULNESS OF SEMI-MARKOV PROCESSES AS MODELS OF THE OPERATION PROCESSES FOR MARINE MAIN ENGINES AND OTHER MACHINES OF SHIP POWER PLANTS
PublicationThe paper describes the properties of semi-Markov processes and the opportunities and benefits from their use as models of the operation processes for marine combustion engines and other machines of ship power plants. The emphasis is put on the importance of the theory of semi-Markov processes for development of the theory of marine combustion engines and other machines of ship power plants, as well as for development of the operational...
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On quasi-compact Markov nets
PublicationAnalizuje się strukturę ergodyczną netów Markowa. W szczególności podano charakteryzację ściśle ergodycznych minimalnych (L-R) netów markowskich na zwartej przestrzeni fazowej. Uzyskano warunki równoważne quasi-zwartości (L-R) netów Markowa, rozszerzając tzw. ergodyczne twierdzenie Lotz'a.
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublicationVarious equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....
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Assesment of operation of ship main diesel engine using the theory of semi-markovian and markov processes.
PublicationTo precisely determine the task it is necessary to specify also its duration time, apart from conditions in which it will be realized. When considering propulsion engine, i.e. the main element of ship propulsion system, especially important becomes not only the problem which amount of energy could be at one's disposal but also within which time interval it could be delivered. Therefore apart from applying the commonly used reliability...
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On residualities in the set of Markov operators on C1
PublicationDowodzi się, że zbiór operatorów Markowa na klasie Schattena 1, które są mieszające w normie, jest normowo gęsty, otwarty. Natomiast w topologii mocno operatorowej operatory Markowa mocno mieszające są zbiorem I kategorii.
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Semi-Markov Approach to the Shipping Safety Modelling
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Strong mixing Markov semigroups on C1 are meager
PublicationDowodzi się, że zbiór tych półgrup operatorów Markowa na klasie Schattena C1, dla których w mocnej topologii operatorowej T(t) jest zbieżne do operatora Markowa Q, gdzie Q jest 1-wymiarową projekcją, jest zbiorem rzadkim w zbiorze wszystkich półgrup Markowa.
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Average Size of a Suffix Tree for Markov Sources
PublicationWe study a suffix tree built from a sequence generated by a Markovian source. Such sources are more realistic probabilistic models for text generation, data compression, molecular applications, and so forth. We prove that the average size of such a suffix tree is asymptotically equivalent to the average size of a trie built over n independentsequences from the same Markovian source. This equivalenceis only known for memoryless...
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Application Isssues of the Semi-Markov Reliability Model
PublicationPredicting the reliability of marine internal combustion engines, for instance, is of particular importance, as it makes it possible to predict their future reliability states based on the information on the past states. Correct reliability prediction is a complex process which consists in processing empirical results obtained from operating practice, complemented by analytical considerations. The process of technical state changes...
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Semi-Markov model of diesel engines' operating process.
PublicationNajistotniejszym problemem eksploatacji silników o zapłonie samoczynnym jest problem racjonalnego (a zwłaszcza optymalnego) sterowania procesem eksploatacji tych silników. Sterowanie takie może ułatwić zastosowanie iteracyjnego algorytmu wyznaczania optymalnych strategii opracowanego przez R.A. Howarda. Wykorzystanie jednak tego algorytmu do sterowania procesem eksploatacji silników wymaga między innymi opracowania modelu procesu...
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Hidden Markov Models for Visual Processing of Marketing Leaflets
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On the mixing property and the ergodic principle for nonhomogeneous Markov chains
PublicationW pracy rozważane są różne typy zachowania granicznego nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym. Badana jest struktura geometryczna zbioru łańcuchów Markowa w normowej i mocnej topologii operatorowej.
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Optimal asynchronous estimation of 2D Gaussian-Markov processes
PublicationW artykule rozważa się problem estymacji trajektorii dwuwymiarowych ciągłoczasowych procesów Gaussa-Markowa na podstawie zaszumionych pomiarów wykonywanych w nierównomiernie rozłożonych chwilach czasu. W przypadku takiego problemu, w każdym cyklu pracy algorytmu należy dokonać dyskretnoczasowej predykcji (analogicznie jak w przypadku filtru Kalmana). Niestety zadanie to może być złożone obliczeniowo. Aby rozwiązać ten problem,...
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Towards More Realistic Probabilistic Models for Data Structures: The External Path Length in Tries under the Markov Model
PublicationTries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP addresses lookup, from data compression (i.e., Lempel- Ziv'77 scheme) to dynamic hashing, from partial-match queries to speech recognition, from leader election algorithms to distributed hashing...
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The semi-Markov model of the process of appearance of sea-going ship propupsion system ability and inability states in application to determining the reliablity of these systems
PublicationThe article presents possible application of the theory of semi-Markov processes in creating the eight-state model of the process of appearance of the propulsion systems ability and inability states on sea-going vessels performing transportation tasks in a relatively long operating time t (t → ∞). The model has been proved to be able to be successfully used for determining the reliability of the abovementioned systems. The probability...
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APPLICATION OF THE THEORY OF SEMI-MARKOV PROCESSES TO DETERMINE A LIMITING DISTRIBUTION OF THE PROCESS OF CHANGES OF ABILITY AND INABILITY STATES OF FUEL SUPPLY SYSTEMS IN HEAVY FUEL DIESEL ENGINES
PublicationThe paper presents applicability of the theory of semi-Markov processes to determine a limiting distribution of the process of changes of technical states of fuel systems for marine engines running on heavy fuel oils. The proposed study of this process includes the components of such fuel systems like: 1 - injectors, 2 - high pressure hoses, 3 - injection pumps, 4 - low pressure hoses, 5 – fine filters, 6 - coarse filters, 7 – fuel-feed...
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A semi-Markov model of fuel combustion process in a Diesel engine
PublicationW artykule przedstawiono czterostanowy model procesu spalania w przestrzeniach roboczych (cylindrach) silników o zapłonie samoczynnym w formie procesu semimarkowskiego, dyskretnego w stanach i ciągłego w czasie. Wartościami tego procesu są stany odpowiadające powszechnie akceptowanym rodzajom spalania w tego rodzaju silnikach a mianowicie takie stany procesu jak: spalanie pełne (całkowite i zupełne), spalanie niezupełne, spalanie...
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Application of theory of semi-Markov processes to determining distribution of probabilistic process of marine accidents resulting from colission of ships
PublicationIn this paper is presented possible application of the theory of semi-Markov processes to elaborating an eight-state model of the process of occurrence of serviceability state and unserviceability states of sea-going ships making critical manoeuvres during their entering and leaving the ports. In the analysis it was taken into account that sea-going ships are in service for a very long time t (t → ∞). The model was elaborated to...
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Quantum-correlation breaking channels, broadcasting scenarios, and finite Markov chains
PublicationOne of the classical results concerning quantum channels is the characterization of entanglementbreakingchannels [M. Horodecki et al., Rev. Math. Phys 15, 629 (2003)]. We address the questionwhether there exists a similar characterization on the level of quantum correlations which may gobeyond entanglement. The answer is fully affirmative in the case of breaking quantum correlationsdown to the, so called, QC (Quantum-Classical)...
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The Matter of Decision-Making Control Over Operation Processes of Marine Power Plant Systems with the Use of their Models in the form of Semi-Markov Decision-Making Processes
PublicationThe article presents the possibility to control the real operation process of an arbitrary device installed in the marine power plant based on the four-state semi-Markov process, being the model of the process, which describes the transition process of operational states of the device and the transition process of its technical states. All these states are precisely defined for the ship main engine (SG). A hypothesis is proposed...
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Investigating Human Visual Behavior by Hidden Markov Models in the Design of Marketing Information
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The time of the first transition of the semi-Markov process in the evaluation of diesel engine operation
PublicationW referacie przedstawiono rozwinięcie prezentowanej w literaturze metody ilościowej oceny działania na przykładzie okrętowego silnika głównego z zapłonem samoczynnym. Według tej interpretacji, działanie silnika może zostać przedstawione jako wielkość fizyczna. W tym aspekcie, na przykładzie okrętowego silnika napędu głównego dokonano oceny przydatności tej wielkości do opisu własności niezawodnościowych silnika. Precyzyjne określenie...
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A model of fuel combustion process in the marine reciprocating engine work space taking into account load and wear of crankshaft-piston assembly and the theory of semi-Markov processes
PublicationThe ar ticle analyses the operation of reciprocal internal combu stion engines, with mar ine engines u sed a s an example. The analysis takes into account types of energy conversion in the work spaces (cylinders) of these engines, loads of their crankshaft-piston assemblies, and types of fuel combustion which can take place in these spaces during engine operation. It is highlighted that the analysed time-dependent loads of marine...
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Limiting distribution of the three-state semi-Markov model of technical state transitions of ship power plant machines and its applicability in operational decision-making.
PublicationThe article presents the three-state semi-Markov model of the process {W(t): t 0} of state transitions of a ship power plant machine, with the following interpretation of these states: s1 – state of full serviceability, s2 – state of partial serviceability, and s3 – state of unserviceability. These states are precisely defined for the ship main engine (ME). A hypothesis is proposed which explains the possibility of application...
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Necessity for and possibility of application of the theory of semi-markov processes to determine reliability of diagnising systems
PublicationW opracowaniu uzasadniono konieczność określenia niezawodności systemów diagnozujących (SDG) do sformułowania diagnozy o stanie dowolnego urządzenia technicznego jako systemu diagnozowanego (SDN). Wykazano, że znajomość niezawodności SDG umożliwia określenie wiarygodności diagnozy. Przyjęto, że wiarygodność diagnozy może być określona jako właściwość diagnozy określająca stopień rozpoznania przez system diagnozujący (SDG) rzeczywistego...
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Applying Hidden Markov Models to Visual Activity Analysis for Simple Digital Control Panel Operations
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Application of hidden Markov models to eye tracking data analysis of visual quality inspection operations
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Możliwość oszacowania niezawodności silników o zapłonie samoczynnym z zastosowaniem teorii procesów semi-Markowa oraz podejmowania decyzji eksploatacyjnych z uwzględnieniem wiarygodności diagnozy o stanie technicznym tego rodzaju silników spalinowych = Possibility of estimating the reliability of diesel engines by applying the theory of semi-Markov processes and making operational decisions by considering reliability of diagnosis on technical state of this sort of combustion engines/
PublicationThe paper presents semi-Markov models of technical state transitions for diesel engines, useful for determining reliability of the engines. A possibility of application of a three-state model with a simplified matrix function, or even a two-state model, to determine reliability of the engines, has been described herein on examples of known from literature semi-Markov models, for the case when appropriate diagnosing systems (SDG)...
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The semi-Markov model of energy state changes of the main marine internal combustion engine and method for evaluating its operation during ships voyage
PublicationPrzedstawiono metodę oceny działania tłokowych silników spalinowych napędu głównego statków morskich, nazywanych silnikami głównymi, działających w różnych warunkach ich eksploatacji. Metoda ta umożliwia obliczenie wartości działania w wyniku zastosowania teorii procesów semimarkowskich i statystyki matematycznej. Znamienne jest to, że działanie wspomnianych silników spalinowych zostało przyrównane do wielkości fizycznej, którą...
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Application of the theory of semi-markov processes to the development of a reliability model of an automotiv vrhicle = Zastosowanie teorii procesów semi-Markowa do opracowania modelu niezawodnościowego samochodu
PublicationW artykule przedstawiono możliwość zastosowania teorii procesów semi-Markowa (semimarkowskich) do opisu niezawodności samochodu, na przykładzie samochodu osobowego. W rozważaniach uwzględniony został samochód, w którym wyróżniono takie węzły konstrukcyjne (zespoły funkcjonalne) jak: silnik z układami zasilania czynnikami energetycznymi (paliwem, olejem smarowym i cieczą chłodzącą), sprzęgło, skrzynia biegów, wał napędowy, most...
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Newton’s Method for the McKendrick-von Foerster Equation
PublicationIn the paper we study an age-structured model which describes the dynamics of one population with growth, reproduction and mortality rates. We apply Newton’smethod to the McKendrick-von Foerster equation in the semigroup setting. We prove its first- and second-order convergence.
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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Two examples of Quantum Dynamical Semigroups
PublicationThe Hamiltonians of the considered bi-partite systems are of the form $$ H_{S,R} = H_S /times 1_R + Q_{S} /times M_R + 1_S /times H_R $$ Subindex $S$ corresponds to the observed system and $R$ to the reservoir (the enviroment of $S$). Two classes of systems are distinguished: the discrete-continuous...
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TEORIA DECYZYJNYCH PROCESÓW SEMI-MARKOWA I JEJ ZASTOSOWANIE W PROJEKTOWANIU I EKSPLOATACJI OKRĘTOWYCH SILNIKÓW GŁÓWNYCH I INNYCH URZĄDZEŃ SIŁOWNI OKRĘTOWYCH
PublicationW referacie zaprezentowano znaczenie teorii procesów semi-Markowa w naukach technicznych, zwłaszcza w teorii niezawodności urządzeń technicznych, teorii bezpieczeństwa ich działania oraz statystycznej teorii podejmowania decyzji eksploatacyjnych. W referacie wyeksponowano także przydatność teorii procesów semi-Markowa w teorii i praktyce eksploatacji wspomnianych urządzeń technicznych na przykładzie tak istotnych urządzeń w transporcie...
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Simple SIR models with Markovian control
PublicationWe consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving...
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Direct chromatographic methods in the context of green analytical chemistry
PublicationWe review analytical protocols based on gas and liquid chromatography (GC and LC), but involving no sample preparation.Green analytical chemistry seeks to minimize negative impacts of analytical chemistry. Direct analytical methods ideally fulfillthis requirement, as they preclude sample preparation - the most polluting step of the analytical procedure.We describe examples of GC methodologies for environmental and food analysis...
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Limits Theorems for Random Walks on Homeo(S1)
PublicationThe central limit theorem and law of the iterated logarithm for Markov chains corresponding to random walks on the space Homeo(S1) of circle homeomorphisms for centered Lipschitz functions and every starting point are proved.
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Straightened characteristics of McKendrick-von Foerster equation
PublicationWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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Mieszanie w klasie niejednorodnych łańcuchów Markowa i kwadratowych operatorów stochastycznych
PublicationRozprawa doktorska poświęcona jest zagadnieniu asymptotycznych własności w klasie nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym oraz w klasie kwadratowych operatorów stochastycznych. W pierwszej kolejności definiowane są różne rodzaje asymptotycznego zachowania (mieszania) niejednorodnych łańcuchów Markowa odpowiadające zbieżności w normowej i mocnej topologii operatorowej oraz omówione są relacje...