Branching Random Walks : École d'Été de Probabilités de Saint-Flour XLII – 2012 / by Zhan Shi.

Format:

Book

Author/Creator:

Shi, Zhan (Mathematician), author.

Series:

École d'Été de Probabilités de Saint-Flour, 0721-5363 ; 2151

Language:

English

Subjects (All):

Probabilities.

Probability Theory and Stochastic Processes.

Local Subjects:

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (X, 133 p. 8 illus., 6 illus. in color.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

Summary:

Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time. Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees. .

Contents:

I Introduction

II Galton–Watson trees

III Branching random walks and martingales

IV The spinal decomposition theorem

V Applications of the spinal decomposition theorem

VI Branching random walks with selection

VII Biased random walks on Galton–Watson trees

A Sums of i.i.d. random variables

References.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

9783319253725

3319253727

OCLC:

1066184452