商品描述
This book presents a broad range of computational techniques based on repeated random sampling, widely known as Monte Carlo methods and sometimes as stochastic simulation. These methods bring together ideas from probability theory, statistics, computer science, and statistical physics, providing tools for solving problems in fields such as operations research, biotechnology, and finance. Topics include the generation and analysis of pseudorandom numbers (which are intended to imitate truly random numbers on a computer), the design and justification of Monte Carlo algorithms, and advanced approaches such as Markov chain Monte Carlo and stochastic optimization. In contrast to deterministic numerical methods, the outcome of a Monte Carlo algorithm is itself random - and one needs the tools of probability and statistics to interpret these results meaningfully. The theoretical foundations, particularly the law of large numbers and central limit theorem, are combined with practical algorithms that reveal both the strengths and subtleties of stochastic simulation. The book includes numerous exercises, both theoretical and computational. Each chapter features step-by-step algorithms, illustrated examples, and results presented through numerical computations, tables, and a variety of plots and figures. All Python code used to produce these results is publicly available, allowing readers to reproduce and explore simulations on their own. Intended primarily for graduate students and researchers, the exposition focuses on core concepts and intuitive understanding, avoiding excessive formalism. The book is suitable both for self-study and as a course text and offers a clear pathway from foundational principles to modern applications.
商品描述(中文翻譯)
本書介紹了一系列基於重複隨機抽樣的計算技術，這些技術廣為人知為蒙地卡羅方法（Monte Carlo methods），有時也稱為隨機模擬（stochastic simulation）。這些方法結合了概率論、統計學、計算機科學和統計物理的思想，提供了解決運籌學、生物技術和金融等領域問題的工具。
主題包括偽隨機數的生成與分析（這些數字旨在模擬計算機上的真正隨機數）、蒙地卡羅算法的設計與證明，以及馬可夫鏈蒙地卡羅（Markov chain Monte Carlo）和隨機優化等先進方法。與確定性數值方法相比，蒙地卡羅算法的結果本身是隨機的，因此需要概率和統計的工具來有意義地解釋這些結果。理論基礎，特別是大數法則（law of large numbers）和中心極限定理（central limit theorem），與實用算法相結合，揭示了隨機模擬的優勢和微妙之處。
本書包含大量的練習題，涵蓋理論和計算。每一章都提供逐步的算法、插圖示例，以及通過數值計算、表格和各種圖形呈現的結果。所有用於生成這些結果的 Python 代碼均可公開獲得，讓讀者能夠自行重現和探索模擬。
本書主要針對研究生和研究人員，重點在於核心概念和直觀理解，避免過度的形式主義。該書適合自學和作為課程教材，並提供從基礎原則到現代應用的清晰路徑。
作者簡介
Pawel Lorek obtained his PhD at the University of Wroclaw in 2007, where he is currently a professor at the Faculty of Mathematics and Computer Science. His main scientific interests include Markov chains (in particular, the rate of convergence to stationarity and duality-based methods), computer security, and probabilistic aspects of machine learning.
Tomasz Rolski obtained his PhD at the University of Wroclaw in 1972, where he is currently a professor at the Faculty of Mathematics and Computer Science. He is the author or co-author of about 90 scientific publications and three books in various areas of applied probability. His main mathematical interests include queueing theory, point processes, ruin theory, and life insurance mathematics.
作者簡介(中文翻譯)
Pawel Lorek 於 2007 年在弗羅茨瓦夫大學（University of Wroclaw）獲得博士學位，目前是數學與計算機科學系的教授。他的主要研究興趣包括馬可夫鏈（特別是收斂到穩態的速率和基於對偶的方法）、計算機安全以及機器學習的概率性方面。
Tomasz Rolski 於 1972 年在弗羅茨瓦夫大學獲得博士學位，目前是數學與計算機科學系的教授。他是約 90 篇科學出版物和三本應用概率各領域書籍的作者或合著者。他的主要數學興趣包括排隊理論、點過程、破產理論和壽險數學。
