Lyapunov Exponents for Branching Processes in a Random Environment: The Effect of Information

We consider multitype branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence of random matrices, which is a notoriously difficult problem. We define Markov chains associated to the branching process, and we construct bounds for the Lyapunov exponent. The bounds are obtained by adding or by removing information: to add information results in a lower bound, to remove information results in an upper bound, and we show that adding less information improves the lower bound. We give a few illustrative examples and we observe that the upper bound is generally more accurate than the lower bounds.


Published in:
Journal Of Statistical Physics, 163, 2, 393-410
Year:
2016
Publisher:
New York, Springer Verlag
ISSN:
0022-4715
Keywords:
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 Record created 2016-07-19, last modified 2018-09-13

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