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Habilitation à diriger des recherches

Equations différentielles stochastiques singulièrement perturbées

Abstract : We consider systems of stochastic differential equations involving two well-separated time scales. We start by establishing, in a general setting, concentration properties of sample paths in a neighbourhood of the slow manifolds of the system's deterministic counterpart. We then study the dynamics in the neighbourhood of a bifurcation point of the slow manifold, in particular in the cases of a saddle-node and of a pitchfork bifurcation. The related phenomena of stochastic resonance and dynamical hysteresis are also studied in detail. Finally, we derive the law of first-passage times through an unstable periodic orbit, for a family of equations which are not limited to the case of well-separated time scales.
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Habilitation à diriger des recherches
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Contributor : Nils Berglund <>
Submitted on : Sunday, January 25, 2004 - 7:04:56 PM
Last modification on : Thursday, March 28, 2019 - 1:30:04 PM
Long-term archiving on: : Tuesday, September 7, 2010 - 4:54:16 PM


  • HAL Id : tel-00004304, version 1



Nils Berglund. Equations différentielles stochastiques singulièrement perturbées. Mathématiques [math]. Université du Sud Toulon Var, 2004. ⟨tel-00004304⟩



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