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 (₀) of probability measures on ₀ with the metric d_TV of total variation, given by

and with the arising Borel-σ-algebra. Thus, we may consider random probability measures on ₀, which are random variables F with values in (₀). Moreover, their mean value and normalized second factorial moment

are now random variables.

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