Stochastic Disorder Problems
暫譯: 隨機無序問題

Shiryaev, Albert N., Poor, H. Vincent, Iacob, Andrei

Stochastic Disorder Problems
  • 出版商: Springer
  • 出版日期: 2019-03-20
  • 售價: $5,030
  • 貴賓價: 9.5 折 $4,779
  • 語言: 英文
  • 頁數: 397
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3030015254
  • ISBN-13: 9783030015251
  • 相關分類: 機率統計學 Probability-and-statistics

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商品描述

This monograph focuses on those stochastic quickest detection tasks in disorder problems that arise in the dynamical analysis of statistical data. These include quickest detection of randomly appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics). There is also currently great interest in quickest detection methods for randomly occurring intrusions in information systems and in the design of defense methods against cyber-attacks. The author shows that the majority of quickest detection problems can be reformulated as optimal stopping problems where the stopping time is the moment the occurrence of disorder is signaled. Thus, considerable attention is devoted to the general theory of optimal stopping rules, and to its concrete problem-solving methods.

The exposition covers both the discrete time case, which is in principle relatively simple and allows step-by-step considerations, and the continuous-time case, which often requires more technical machinery such as martingales, supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. The last chapter presents applications to financial markets.

Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.

商品描述(中文翻譯)

這本專著專注於隨機的最快偵測任務，這些任務出現在統計數據的動態分析中的混亂問題中。這些任務包括隨機出現目標的最快偵測、自發產生效應的最快偵測，以及金融數學中的套利問題。目前，對於隨機發生的入侵在資訊系統中的最快偵測方法以及設計對抗網路攻擊的防禦方法也引起了極大的興趣。作者顯示，大多數最快偵測問題可以重新表述為最佳停頓問題，其中停頓時間是混亂發生被信號化的時刻。因此， considerable attention is devoted to the general theory of optimal stopping rules, and to its concrete problem-solving methods.

本書的闡述涵蓋了離散時間的情況，這在原則上相對簡單，並允許逐步考慮，以及連續時間的情況，這通常需要更多的技術工具，如鞅、超鞅和隨機積分。重點放在布朗運動的成熟工具上，這使得許多問題的精確解決成為可能。最後一章介紹了對金融市場的應用。

對於對概率、決策理論和統計序列分析感興趣的研究人員和研究生來說，本書將會非常有用。

作者簡介

Albert N. Shiryaev is Chief Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences and Head of the Department of Probability Theory in the Mechanics and Mathematics Faculty at Lomonosov Moscow State University. He is the author of several books, including Problems in Probability [translated by Andrew Lyasov], Optimal Stopping Rules [translated by A.B. Aries], and Statistics of Random Processes [with Robert S. Liptser]. He was the recipient of the A.A.MarkovPrize in 1974, of the A.N.Kolmogorov Prize in 1994, and of the Golden P.L.Chebyshev Medal of the Russian Academy of Science in 2017.


作者簡介(中文翻譯)

阿爾伯特·N·希里亞耶夫（Albert N. Shiryaev）是俄羅斯科學院斯捷克洛夫數學研究所的首席科學研究員及概率論和數理統計教授，同時也是莫斯科國立大學機械與數學學院概率論系的系主任。他著有多本書籍，包括《概率問題》（Problems in Probability，譯者：安德魯·利亞索夫）、《最佳停止規則》（Optimal Stopping Rules，譯者：A.B. Aries）以及《隨機過程的統計》（Statistics of Random Processes，與羅伯特·S·利普特塞爾合作）。他於1974年獲得A.A.馬爾可夫獎，1994年獲得A.N.科爾莫哥洛夫獎，並於2017年獲得俄羅斯科學院金獎P.L.切比雪夫獎章。

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