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The chapter is an introduction to the book devoted to studying ergodic theorems with explicit power and exponential upper bounds for convergence rates for Markov chains, renewal, and regenerative processes obtained using the coupling method and the method of test functions. It informally presents the main problems, methods, and algorithms that comprise the book’s contents, gives simple examples illustrated by 15 figures, and tries to show the logic and ideas underlying the coupling method and the method of test functions and their applications for obtaining ergodic theorems with explicit upper bounds for convergence rates for Markov chains, renewal, and regenerative processes, as well as to explain the meaning of the results presented in the book.

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Introduction

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  • 发表日期：

    2025年

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  • Dmitrii Silvestrov

摘要

The chapter is an introduction to the book devoted to studying ergodic theorems with explicit power and exponential upper bounds for convergence rates for Markov chains, renewal, and regenerative processes obtained using the coupling method and the method of test functions. It informally presents the main problems, methods, and algorithms that comprise the book’s contents, gives simple examples illustrated by 15 figures, and tries to show the logic and ideas underlying the coupling method and the method of test functions and their applications for obtaining ergodic theorems with explicit upper bounds for convergence rates for Markov chains, renewal, and regenerative processes, as well as to explain the meaning of the results presented in the book.