From classical to modern probability : cimpa summer school 2001从古典到现代可能性
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作者： Pierre Picco，Jaime San Martin著
出 版 社：
出版时间： 2004-1-1字数：版次：页数： 219印刷时间： 2004/01/01开本： 16开印次：纸张： 胶版纸I S B N ： 9783764321697包装： 精装内容简介
This volume is based on the lecture notes of six courses delivered at a CIMPA Summer School in Temuco, Chile, in January 2001. The courses are: asymptotic of the heat kernel in unbounded domains; spin systems with long range interactions; non-linear Dirichlet problem and non-linear integration; first-passage percolation; central limit theorem for Markov processes; stochastic orders and stopping times in Brownian motion. The level of each course is that of a graduate course, but the material will also be of interest for the specialist.
目录
Contents
Foreword
Introduction
The game of Dudo
P. Collet
Asymptotic of the Heat Kernel in Unbounded Domains
1 Introduction
2 Ratio theorem for domains with harmonic cone C~ of dimension 1
3 Benedicks domains
References
A. De Masi
Spin Systems with Long Range Interactions
1 Ising spin systems
2 Phase transition
3 Time evolution
References
C. Dellaeherie
Nonlinear Dirichlet Problem and Nonlinear Integration
1 Generalities
2 Preliminaries on capacities
3 Radon capacities
4 Lusin capacities
5 Answering the questions and last words
References
H. Kesten
First-Passage Percolation
1 The basic model and the shape model
2 Exponential bounds for large deviations
3 Bounds of moderate deviations
References
C. Landim
Central Limit Theorem for Markov Processes
1 Introduction
2 A warming-up example
3 Central limit theorem for Markov processs
4 Regularity of the diffusion coefficient
References
I Meilijson
Stochastic Orders and Stopping Times in Brownian Motion
1 Introduction
2 Martingales and stochastic orders
3 Skorohod embeddings in standard Brownian motion
4 A maximal property of Azema-Yor stopped Brownian motion
5 Practical description of the optimal stopping time for
the look-back American put option problem
References