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Titlebook: Probability Theory; A Comprehensive Cour Achim Klenke Textbook 2020Latest edition The Editor(s) (if applicable) and The Author(s), under ex

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发表于 2025-3-21 19:58:49 | 显示全部楼层 |阅读模式
书目名称Probability Theory
副标题A Comprehensive Cour
编辑Achim Klenke
视频video
概述Provides a complete introduction to probability theory, including measure theory and scientific applications.New updated edition includes concise summaries of each section, as well as outlooks and que
丛书名称Universitext
图书封面Titlebook: Probability Theory; A Comprehensive Cour Achim Klenke Textbook 2020Latest edition The Editor(s) (if applicable) and The Author(s), under ex
描述This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory..Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms.Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as:. . .limit theorems for sums of random variables. .martingales. .percolation. .Markov chains and electrical networks. .construction of stochastic processes. .Poisson point process and infinite divisibility. .large deviation principles and statistical physics. .Brownian motion. .stochastic integrals and stochastic differential equations.. . The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts..This third edition has been carefully extended and includes new features, such as concise summaries
出版日期Textbook 2020Latest edition
关键词Central Limit Theorem; Markov Chain; Martingales; Stochastic Processes; Stochastic Differential Equation
版次3
doihttps://doi.org/10.1007/978-3-030-56402-5
isbn_softcover978-3-030-56401-8
isbn_ebook978-3-030-56402-5Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Infinitely Divisible Distributions,normal distribution is the limit of . sums of independent and identically distributed random variables (central limit theorem). In the second section, we investigate briefly which subclass of the infinitely divisible measures on the real line shares this property.
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Independence,ion on the integer lattice): using independent coin flips the individual bonds in the lattice are either kept or deleted. The question of interest is whether there is an infinite connected component or not.
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Backwards Martingales and Exchangeability,random. At the second stage, i.i.d. random variables with distribution . are implemented..We first define the notion of exchangeability. Then we consider backwards martingales and prove the convergence theorem for them. This is the cornerstone for the proof of de Finetti’s theorem.
发表于 2025-3-23 05:25:25 | 显示全部楼层
Markov Chains,mber of returns to the origin of simple random walk on multidimensional integer lattices..The connection with discrete potential theory will be investigated later, in Chap. .. Some readers might prefer to skip the somewhat technical construction of general Markov processes in Sect. 17.1.
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