The transition point in the zero noise limit for a 1D Peano example

François Delarue; Franco Flandoli

doi:10.3934/dcds.2014.34.4071

Article Contents

2014, Volume 34, Issue 10: 4071-4083. Doi: 10.3934/dcds.2014.34.4071

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The transition point in the zero noise limit for a 1D Peano example

François Delarue^1, and
Franco Flandoli^2,

1.
Laboratoire J.A. Dieudonné, UMR CNRS-UNS 7351, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 2
2.
Dipartimento Matematica, Via Buonarroti 1c, C.A.P. 56127, Pisa

Received: February 2013

Revised: April 2013

Published: October 2014

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Abstract

The zero-noise result for Peano phenomena of Bafico and Baldi (1982) is revisited. The original proof was based on explicit solutions to the elliptic equations for probabilities of exit times. The new proof given here is purely dynamical, based on a direct analysis of the SDE and the relative importance of noise and drift terms. The transition point between noisy behavior and escaping behavior due to the drift is identified.

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Mathematics Subject Classification: Primary: 60H10, 34A12; Secondary: 60F99, 60J65.

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