Noisy heteroclinic networks

Yuri Bakhtin

doi:10.1007/s00440-010-0264-0

Noisy heteroclinic networks

Yuri Bakhtin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distribution in a special topology to a piecewise constant process that jumps between saddle points along the heteroclinic orbits of the network. We also obtain precise asymptotics for the exit measure for a domain containing the starting point of the diffusion.

Original language	English (US)
Pages (from-to)	1-42
Number of pages	42
Journal	Probability Theory and Related Fields
Volume	150
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-010-0264-0
State	Published - Jun 2011

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-010-0264-0

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AB - We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distribution in a special topology to a piecewise constant process that jumps between saddle points along the heteroclinic orbits of the network. We also obtain precise asymptotics for the exit measure for a domain containing the starting point of the diffusion.

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Noisy heteroclinic networks

Abstract

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