Translated from Russian, this book is an up-to-date account of ergodicity and of the stability of random processes. Important examples are Markov chains (MC) in arbitrary state space, stochastic recursive sequences (SRC) and MC in random environments (MCRI), as well as their continous time analogues.
Table of Contents:
GENERAL THEOREMS ON ERGODICITY AND STABILITY. General Ergodicity and Stability Theorems for Harris Irreducible Markov Chains.
Ergodicity and Stability Conditions for Markov Chains Not Related to Harris Irreducibility.
Stochastically Recursive Sequences and Their Generalizations (Markov Chains in Random Environments).
Ergodicity of Stochastic Processes in Continuous and Discrete Time.
ERGODICITY AND STABILITY OF MULTI-DIMENSIONAL MARKOV CHAINS AND MARKOV PROCESSES.
Conditions fo Positive Recurrence and Ergodicity Multi-Dimensional Markov Chains and the Method of Lyapunov Functions.
A Description of Multi-Dimensional Processes to be Studied. Ergodicity, Stability, and Probabilities of Large Deviations of One-Dimensional Markov Chains.
Ergodicity and Stability of Two-Dimensional Markov Chains and the Method of Approaching Times.
Markov Chains in Positive Octants of Three and More Dimensions and the Method of Approaching Times.
Ergodicity and Stability of Multi-Dimensional Diffusions and Jump Markov Processes.
Transition Phenomena for One-Dimensional Markov Chains: Approximation of Stationary Distributions.
AUXILIARY PROPOSITIONS. ERGODICITY AND STABILITY OF QUEUEING AND COMMUNICATION NETWORKS.
Estimates of Moments and Probabilities of Large Deviations for Certain Random Walks.
Ergodicity and Stability of Queueing and Communication Networks.
References.
Subject Index.
About the Author :
Aleksandr Alekseevich Borovkov is a Russian mathematician. Borovkov received his Russian candidate degree in 1959 under Andrey Kolmogorov at Moscow State University and his Russian doctorate in 1963.
