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Spiking and collapsing in large noise limits of SDE's

Abstract : We analyze strong noise limit of some stochastic differential equations. We focus on the particular case of Belavkin equations, arising from quantum measurements, where Bauer and Bernard pointed out an intriguing behavior. As the noise grows larger, the solutions exhibits locally a collapsing, that is to say converge to jump processes, very reminiscent of a metastability phenomenon. But surprisingly the limiting jump process is decorated by a spike process. We completely prove these statements for an archetypal one dimensional diffusion. The proof is robust and can easily be adapted to a large class of one dimensional diffusions.
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Contributor : Reda Chhaibi <>
Submitted on : Thursday, January 10, 2019 - 9:33:36 AM
Last modification on : Friday, March 27, 2020 - 3:06:03 AM

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C. Bernardin, R. Chetrite, Reda Chhaibi, J. Najnudel, C. Pellegrini. Spiking and collapsing in large noise limits of SDE's. 2019. ⟨hal-01976435⟩



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