First exit times of SDEs driven by stable Lévy processes

P. Imkeller and I. Pavlyukevich

Stochastic Processes and their Applications, 2006, vol. 116, issue 4, 611-642

Abstract: We study the exit problem of solutions of the stochastic differential equation from bounded or unbounded intervals which contain the unique asymptotically stable critical point of the deterministic dynamical system . The process L is composed of a standard Brownian motion and a symmetric [alpha]-stable Lévy process. Using probabilistic estimates we show that, in the small noise limit [epsilon]-->0, the exit time of X[epsilon] 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.

Keywords: Lévy; process; Lévy; flight; First; exit; Exit; time; law; [alpha]-Stable; process; Kramers'; law; Infinitely; divisible; distribution; Extreme; events (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (6)

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