# American Institute of Mathematical Sciences

October  2014, 34(10): 4071-4083. doi: 10.3934/dcds.2014.34.4071

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

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

Received  February 2013 Revised  April 2013 Published  April 2014

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.
Citation: François Delarue, Franco Flandoli. The transition point in the zero noise limit for a 1D Peano example. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4071-4083. doi: 10.3934/dcds.2014.34.4071
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