November 2017
Intermediate to advanced
306 pages
6h 24m
English
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 dTV 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 ...