First exit times of solutions of non-linear stochastic differential equations driven by symmetric Levy processes with alpha-stable components

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dc.creatorImkeller, Peter
dc.creatorPavlyukevich, Ilya
dc.date2004-09-15
dc.date2006-01-31
dc.date.accessioned2026-07-07T06:38:48Z
dc.date.available2026-07-07T06:38:48Z
dc.descriptionWe study the exit problem of solutions of the stochastic differential equation dX(t)=-U'(X(t))dt+epsilon dL(t) from bounded or unbounded intervals which contain the unique asymptotically stable critical point of the deterministic dynamical system dY=-U'(Y) dt. The process L is composed of a standard Brownian motion and a symmetric alpha-stable Levy process. Using probabilistic estimates we show that in the small noise limit epsilon->0, the exit time of X from an interval is an exponentially distributed random variable and determine its expected value. Due to the heavy-tail nature of the alpha-stable component of L, the results differ strongly from the well known case in which the deterministic dynamical system undergoes purely Gaussian perturbations.
dc.descriptionSlightly revised version. To appear in Stochastic Processes and their Applications. 24 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0409246
dc.identifierhttp://arxiv.org/abs/math/0409246
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100865
dc.subjectProbability
dc.subjectDynamical Systems
dc.subjectData Analysis, Statistics and Probability
dc.subject60E07, 60F10, 60G40, 60G51, 60G52 60H10, 60J75, 60K40, 86A17
dc.titleFirst exit times of solutions of non-linear stochastic differential equations driven by symmetric Levy processes with alpha-stable components
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