數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] pdf epub mobi txt 電子書 下載 2025

圖書介紹


數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart]

簡體網頁||繁體網頁
[美] 杜布(Doob J.L.) 著



下載連結1
下載連結2
下載連結3
    

想要找書就要到 靜流書站
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

發表於2025-05-30


類似圖書 點擊查看全場最低價

齣版社: 世界圖書齣版公司
ISBN:9787510058417
版次:1
商品編碼:11273583
包裝:平裝
外文名稱:Classical Potential Theory and Its Probabilistic Counterpart
開本:24開
齣版時間:2013-03-01
用紙:膠版紙
頁數:846
正文語種:英文

數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2025

相關圖書



數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2025

數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] pdf epub mobi txt 電子書 下載



具體描述

內容簡介

  Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe with jaun- diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory.For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super- martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) invomng the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and,so on.

內頁插圖

目錄

Introduction
Notation and Conventions
Part 1
Classical and Parabolic Potential Theory
Chapter I
Introduction to the Mathematical Background of Classical Potential Theory
1.The Context of Green's Identity
2.Function Averages
3.Harmonic Functions
4.Maximum-Minimum Theorem for Harmonic Functions
5.The Fundamental Kernel for RN and Its Potentials
6.Gauss Integral Theorem
7.The Smoothness of Potentials ; The Poisson Equation
8.Harmonic Measure and the Riesz Decomposition
Chapter II
Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions
1.The Green Function of a Ball; The Poisson Integral
2.Hamack's Inequality
3.Convergence of Directed Sets of Harmonic Functions
4.Harmonic, Subharmonic, and Superharmoruc Functions
5.Minimum Theorem for Superharmonic Functions
6.Application of the Operation TB
7.Characterization of Superharmonic Functions in Terms of Harmonic Functions
8.Differentiable Superharmonic Functions
9.Application of Jensen's Inequality
10.Superharmonic Funaions on an Annulus
II.Examples
12.The Kelvin Transformation
13.Greenian Sets
14.The L1(uB_) and D(uB_) Classes of Harmonic Functions on a Ball B; The
Riesz-Herglotz Theorem
15.The Fatou Boundary Limit Theorem
16.Minimal Harmonic Functions
Chapter III
Infima of Families of Superharmonic Functidns
1.Least Superharmonic Majorant (LM) and Greatest Subharmonic Minorant (GM)
2.Generalization of Theorem I
3.Fundamental Convergence Theorem (Preliminary Version)
4.The Reduction Operation
5.Reduction Properties
6.A Smallness Property of Reductions on Compact Sets
7.The Natural (Pointwise) Order Decomposition for Positive Superharmonk
Functions
Chapter 1V
Potentials on Special Open Sets
1.Special Open Sets, and Potentials on Them
2.Examples
3.A Fundamental Smallness Property of Potentials
4.Increasing Sequences of Potentials
5.Smoothing of a Potential
6.Uniqueness of the Measure Determining a Potential
7.Riesz Measure Associated with a Superharmonic Function
8.Riesz Decomposition Theorem
9.Counterpart for Superharmonic Functions on R2 ofthe Riesz
Decomposition
10.An Approximation Theorem
Chapter V
Polar Sets and Their Applications
1.Definition
2.Superharmonic Functions Associated with a Polar Set
3.Countable Unions of Polar Sets
4.Properties ofPolar Sets
5.Extension of a Superharmonic Function
6.Greenian Sets in IR2 as the Complements of Nonpolar Sets
7.Superharmonic Function Minimum Theorem (Extension of Theorem I1.5)
8.Evans-Vasilesco Theorem
9.Approximation of a Potential by Continuous Potentials
10.The Domination Principle
I1.The Infinity Set of a Potential and the Riesz Measure
……

Part 2
Probabilistic Countrepart of Part 1
Part 3
數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] 下載 mobi epub pdf txt 電子書

數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] pdf epub mobi txt 電子書 下載
想要找書就要到 靜流書站
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

用戶評價

評分

Doob概率界的牛人,他的這本書絕對稱得上巨著,概率必備的專業書籍,

評分

評分

包裝印刷質量很好,希望這樣的書多一些纔好

評分

評分

Doob概率界的牛人,他的這本書絕對稱得上巨著,概率必備的專業書籍,

評分

評分

一本好書,送貨速度很快

評分

評分

類似圖書 點擊查看全場最低價

數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] pdf epub mobi txt 電子書 下載


分享鏈接


去京東購買 去京東購買
去淘寶購買 去淘寶購買
去噹噹購買 去噹噹購買
去拼多多購買 去拼多多購買


數學經典教材:經典位勢論及其對應的概率論(影印版)(英文版) [Classical Potential Theory and Its Probabilistic Counterpart] bar code 下載
扫码下載





相關圖書




本站所有內容均為互聯網搜索引擎提供的公開搜索信息,本站不存儲任何數據與內容,任何內容與數據均與本站無關,如有需要請聯繫相關搜索引擎包括但不限於百度google,bing,sogou

友情鏈接

© 2025 book.coffeedeals.club All Rights Reserved. 靜流書站 版權所有