From classical to modern probability : cimpa summer school 2001从古典到现代可能性 pdf 在线 2025 epub 免费 书籍 下载

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.

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

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