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Random Walk "A Modern Introduction"

A Modern Introduction

Random Walk "A Modern Introduction". A Modern Introduction

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  • ISBN:9780521519182
  • Editorial: Cambridge University Press
  • Fecha de la edición:
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  • Dimensiones: 0 cm x 0 cm
  • Nº Pág.:376
  • Idiomas:Ingles,Inglés

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Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

Preface
1 Introduction 1
1.1 Basic definitions 1
1.2 Continuous-time random walk 6
1.3 Other lattices 7
1.4 Other walks 11
1.5 Generator 11
1.6 Filtrations and strong Markov property 14
1.7 A word about constants 17
2 Local central limit theorem 21
2.1 Introduction 21
2.2 Characteristic functions and LCLT 25
2.2.1 Characteristic functions of random variables in Rd 25
2.2.2 Characteristic functions of random variables in Zd 27
2.3 LCLT-characteristic function approach 28
2.3.1 Exponential moments 46
2.4 Some corollaries of the LCLT 51
2.5 LCLT-combinatorial approach 58
2.5.1 Stirling's formula and one-dimensional walks 58
2.5.2 LCLT for Poisson and continuous-time walks 64
3 Approximation by Brownian motion 72
3.1 Introduction 72
3.2 Construction of Brownian motion 74
3.3 Skorokhod embedding 79
3.4 Higher dimensions 82
3.5 An alternative formulation 84
4 The Green's function 87

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