Hybrid Switching Diffusions: Properties and Applications
暫譯: 混合切換擴散：特性與應用

Nguyen, Hai-Dang, Yin, George, Zhu, Chao

Hybrid Switching Diffusions: Properties and Applications
  • 出版商: Springer
  • 出版日期: 2025-11-12
  • 售價: $6,460
  • 貴賓價: 9.5 折 $6,137
  • 語言: 英文
  • 頁數: 541
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031933028
  • ISBN-13: 9783031933028
  • 相關分類: 工程數學 Engineering-mathematics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This thoroughly revised and expanded edition presents a comprehensive study of hybrid switching diffusion processes and their wide-ranging applications. These processes, which combine continuous dynamics with discrete events, are essential for modeling complex systems influenced by random environments. They have broad applications in such fields as wireless communications, signal processing, queueing networks, production planning, ecosystems, financial engineering, and large-scale system optimization.

Since the publication of the first edition, the study of hybrid switching diffusions has made significant strides, with new theoretical breakthroughs and emerging applications in ecology and population biology. This edition incorporates these advancements, refining and expanding several key chapters. Notably, it introduces

    a new chapter on switching processes with past dependence, extending the theoretical framework to account for historical states in the switching process. a new chapter on mathematical biology applications, demonstrating the relevance of hybrid switching diffusions in biological modeling.

In addition to covering fundamental topics such as existence and uniqueness of solutions, recurrence, ergodicity, invariant measures, and stability, this edition further explores numerical methods and two-time-scale models.

This book is an essential resource for applied mathematicians, probabilists, systems engineers, control scientists, operations researchers, and financial analysts. It is also well-suited for graduate courses on stochastic processes and hybrid systems.

The new edition offers researchers and practitioners a robust and versatile framework, driving significant advancements and broadening the application of stochastic analysis to real-world challenges.

商品描述(中文翻譯)

這本經過徹底修訂和擴充的版本提供了對混合切換擴散過程及其廣泛應用的全面研究。這些過程結合了連續動態和離散事件，對於建模受隨機環境影響的複雜系統至關重要。它們在無線通信、信號處理、排隊網絡、生產規劃、生態系統、金融工程和大規模系統優化等領域有著廣泛的應用。

自第一版出版以來，混合切換擴散的研究取得了顯著進展，出現了新的理論突破和在生態學及種群生物學中的新興應用。本版納入了這些進展，對幾個關鍵章節進行了精煉和擴展。特別是，它引入了：

- 一個關於具有過去依賴的切換過程的新章節，擴展了理論框架以考慮切換過程中的歷史狀態。
- 一個關於數學生物學應用的新章節，展示了混合切換擴散在生物建模中的相關性。

除了涵蓋存在性和唯一性、重返性、遍歷性、不變測度和穩定性等基本主題外，本版還進一步探討了數值方法和雙時間尺度模型。

這本書是應用數學家、機率學家、系統工程師、控制科學家、運籌學研究者和金融分析師的重要資源。它也非常適合用於隨機過程和混合系統的研究生課程。

新版本為研究人員和實務工作者提供了一個強大而多功能的框架，推動了顯著的進展，並擴大了隨機分析在現實挑戰中的應用。

作者簡介

Hai-Dang Nguyen received the B.S. degree in mathematics from the VNU, Hanoi University of Science, Hanoi, Vietnam, in 2008, and the Ph.D. in applied mathematics from Wayne State University, Detroit, MI, USA, in 2018. He joined the University of Alabama, Tuscaloosa, AL, USA, in 2018 as an Assistant Professor and was promoted to Associate Professor, in 2022. His research interests include stochastic systems and applications, mathematical biology, and stochastic control. Dr. Nguyen was the recipient of SIAM Activity Group on Control and Systems Theory Prize in 2019. He is an Associate Editor of Nonlinear Analysis: Hybrid Systems and SIAM Journal
on Control and Optimization.

George Yin received the B.S. degree in mathematics from the University of Delaware in 1983, the M.S. degree in electrical engineering, and the Ph.D. degree in applied mathematics from Brown University in 1987. He joined the Department of Mathematics, Wayne State University in 1987, and became Professor in 1996 and University Distinguished Professor in 2017. He moved to the University of Connecticut in 2020. He was the Editor-in-Chief of SIAM Journal on Control and Optimization from 2018-2023, and is/was on editorial board of many other journals. He is a Fellow of IEEE, a Fellow of IFAC, and a Fellow of SIAM.

Chao Zhu received his B.S. and M.S. degrees in mathematics from East China Normal University, Shanghai, China, in 1999 and 2002, respectively, and his Ph.D. in mathematics from Wayne State University in 2007, under the supervision of Prof. George Yin. He joined the Department of Mathematical Sciences, the University of Wisconsin Milwaukee in 2007 and became a Professor in 2018. He is currently serving on the editorial boards of three journals. His research interests include stochastic analysis, and stochastic control and their applications in areas such as mathematical nance, mathematical biology, and risk management.

作者簡介(中文翻譯)

Hai-Dang Nguyen於2008年獲得越南河內科學大學（VNU, Hanoi University of Science）數學學士學位，並於2018年在美國密西根州底特律的韋恩州立大學（Wayne State University）獲得應用數學博士學位。他於2018年加入美國阿拉巴馬州塔斯卡盧薩的阿拉巴馬大學擔任助理教授，並於2022年晉升為副教授。他的研究興趣包括隨機系統及其應用、數學生物學和隨機控制。Nguyen博士於2019年獲得SIAM控制與系統理論活動小組獎。他是《非線性分析：混合系統》（Nonlinear Analysis: Hybrid Systems）和《SIAM控制與優化期刊》（SIAM Journal on Control and Optimization）的副編輯。

George Yin於1983年獲得德拉瓦大學（University of Delaware）數學學士學位，並於1987年獲得布朗大學（Brown University）電機工程碩士學位及應用數學博士學位。他於1987年加入韋恩州立大學數學系，並於1996年成為教授，於2017年成為大學傑出教授。他於2020年轉至康乃爾大學（University of Connecticut）。他曾擔任《SIAM控制與優化期刊》的主編（Editor-in-Chief）從2018年至2023年，並曾在許多其他期刊的編輯委員會中任職。他是IEEE、IFAC和SIAM的會士。

Chao Zhu於1999年和2002年分別在中國上海的華東師範大學獲得數學學士和碩士學位，並於2007年在韋恩州立大學獲得數學博士學位，指導教授為George Yin教授。他於2007年加入威斯康辛大學密爾瓦基分校（University of Wisconsin Milwaukee）數學科學系，並於2018年成為教授。他目前擔任三本期刊的編輯委員會成員。他的研究興趣包括隨機分析、隨機控制及其在數學金融、數學生物學和風險管理等領域的應用。

類似商品