Bibliographic Details
| Title: |
Lyapunov Exponents for Branching Processes in a Random Environment: The Effect of Information. |
| Authors: |
Hautphenne, Sophie sophie.hautphenne@epfl.ch, Latouche, Guy1 latouche@ulb.ac.be |
| Superior Title: |
Journal of Statistical Physics. Apr2016, Vol. 163 Issue 2, p393-410. 18p. |
| Subject Terms: |
*LYAPUNOV exponents, *MATRICES (Mathematics), *MARKOV random fields, *EXPONENTS, *MATHEMATICAL bounds |
| Abstract: |
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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Academic Search Premier |