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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

2Branching Processes in Random Environment

2.1. Introduction

Now we introduce environmental stochasticity into our branching models. For this purpose, we endow the space images(images0) of probability measures on images0 with the metric dTV of total variation, given by

Image

and with the arising Borel-σ-algebra. Thus, we may consider random probability measures on images0, which are random variables F with values in images(images0). Moreover, their mean value and normalized second factorial moment

Image

are now random variables.

DEFINITION 2.1.– A sequence images = {F1, F2, …} of random probability measures on 0 is called a random environment ...

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ISBN: 9781786302526Purchase book