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

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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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