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Discrete Time Branching Processes in Random Environment
book

Discrete Time Branching Processes in Random Environment

by Götz Kersting, Vladimir Vatutin
November 2017
Intermediate to advanced content levelIntermediate to advanced
306 pages
6h 24m
English
Wiley-ISTE
Content preview from Discrete Time Branching Processes in Random Environment

4Properties of Random Walks

4.1. Introduction

The study of BPREs essentially uses properties of the ordinary random walk S : = {Sn, n ≥ 0} with S0 := 0. This chapter contains some basic results needed in the sequel.

To begin with, we introduce four sequences of random variables related to S. Let

Image

and

Image

be the sequences of strict descending ladder epochs of the random walk and let

Image

be the sequences of weak descending ladder epochs.

In a similar way, we specify the sequences of strict ascending ladder epochs

Image

and weak ascending ladder epochs

Image

The random variables image and image are called ladder heights. Ladder epochs and ladder heights will repeatedly appear in our subsequent arguments. Rather often they will occur when using the so-called duality principle, which we formulate as a theorem.

THEOREM ...

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Publisher Resources

ISBN: 9781786302526Purchase book