内容

目次

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.