Coupling and Ergodic Theorems for Semi-Markov-Type Processes I: Markov Chains, Renewal, and Regenerative Processes
暫譯: 半馬可夫型過程的耦合與遍歷定理 I：馬可夫鏈、更新與再生過程

Silvestrov, Dmitrii

Coupling and Ergodic Theorems for Semi-Markov-Type Processes I: Markov Chains, Renewal, and Regenerative Processes
  • 出版商: Springer
  • 出版日期: 2025-10-27
  • 售價: $8,730
  • 貴賓價: 9.5 折 $8,294
  • 語言: 英文
  • 頁數: 611
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031893107
  • ISBN-13: 9783031893100
  • 相關分類: 機率統計學 Probability-and-statistics

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商品描述

Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications.

This volume delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates, focusing on Markov chains, renewal processes, and regenerative processes. The book offers a powerful and constructive probabilistic framework by employing the elegant coupling method in conjunction with test functions. Theoretical findings are illustrated with applications to perturbed stochastic networks, alternating Markov processes, risk processes, quasi-stationary distributions, and the renewal theorem, all of which feature explicit convergence rate bounds.

Many results presented here are groundbreaking, appearing in publication for the first time. This is the first volume of a two-volume monograph dedicated to ergodic theorems. While this volume centers on Markovian and regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation.

Designed with researchers and advanced students in mind, the content is thoughtfully structured by complexity, making it suitable for self-study or as a resource for upper-level coursework. Each chapter is self-contained and complemented by a comprehensive bibliography, ensuring its value as a long-lasting reference. An essential resource for theoretical and applied research, this book significantly contributes to the field of stochastic processes and will remain a key reference for years to come.

商品描述(中文翻譯)

遍歷定理是隨機過程理論及其應用的基石。本書深入探討遍歷定理，提供明確的收斂速率的冪次和指數上界，重點關注馬可夫鏈、更新過程和再生過程。該書通過結合優雅的耦合方法與測試函數，提供了一個強大且具建設性的概率框架。理論發現通過應用於擾動隨機網絡、交替馬可夫過程、風險過程、準穩態分佈和更新定理來進行說明，所有這些都具有明確的收斂速率界限。

這裡呈現的許多結果都是開創性的，首次發表。本書是專門針對遍歷定理的兩卷專著的第一卷。雖然本卷集中於馬可夫和再生模型，但第二卷將範圍擴展到半馬可夫過程和具有半馬可夫調制的多交替再生過程。

本書旨在為研究人員和高級學生設計，內容按複雜性精心結構，適合自學或作為高級課程的資源。每一章都是獨立的，並附有全面的參考書目，確保其作為長期參考的價值。本書是理論和應用研究的重要資源，對隨機過程領域做出了顯著貢獻，並將在未來幾年內成為關鍵參考資料。

作者簡介

Dmitrii Silvestrov graduated from Kiev University (1968, Mathematics), Candidate of Science [PhD], (1969, Mathematical Statistics), and Doctor of Science (1972, Mathematical Statistics). Awarded the Prize of the Moscow Mathematical Society (1973) and the Ukrainian Ostrovsky Prize (1977) for work on stochastic processes. Lecturer and Senior Lecturer (1970-1974), Professor (1974-1992, Department of Probability and Mathematical Statistics) and Head of the Statistical Research Centre (1980-1990) at Kiev University. Guest scientist at Umeå University (1991-1992), Senior lecturer at Luleå University of Technology (1992-1994) and at Umeå University (1994-1999). Visiting professor at the Hebrew University of Jerusalem (1993), University of Turku (1998), and University of Rome "La Sapienza" (2015). Professor at the Mälardalen University from 1999 (Emeritus Professor from 2012) and Stockholm University from 2009 (Emeritus Professor from 2016). Member of the editorial boards of the journals "Theory of Probability and Mathematical Statistics" and "Theory of Stochastic Processes". Coordinator of the four EU Tempus Projects. The main research areas are stochastic processes, actuarial and financial mathematics, and statistical software. Author of 13 books and more than 170 research papers. Supervised 22 doctoral students who subsequently obtained PhD degrees.

作者簡介(中文翻譯)

德米特里·西爾維斯特羅夫於基輔大學畢業（1968年，數學），獲得科學候選人學位[博士]（1969年，數理統計），並於1972年獲得科學博士學位（數理統計）。因在隨機過程方面的研究而獲得莫斯科數學學會獎（1973年）和烏克蘭奧斯特羅夫斯基獎（1977年）。曾擔任基輔大學講師和高級講師（1970-1974年）、教授（1974-1992年，概率與數理統計系）及統計研究中心主任（1980-1990年）。曾任烏梅奧大學的客座科學家（1991-1992年）、盧勒奧科技大學的高級講師（1992-1994年）及烏梅奧大學的高級講師（1994-1999年）。曾擔任耶路撒冷希伯來大學（1993年）、土耳其大學（1998年）及羅馬大學「拉薩比恩扎」（2015年）的訪問教授。自1999年起擔任馬拉爾達倫大學教授（自2012年起為名譽教授）及斯德哥爾摩大學教授（自2009年起，2016年起為名譽教授）。是《概率與數理統計理論》和《隨機過程理論》期刊的編輯委員會成員。協調四個歐盟Tempus項目。主要研究領域包括隨機過程、精算與金融數學以及統計軟體。著有13本書和170多篇研究論文。指導了22名博士生，這些學生隨後獲得博士學位。

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