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The estimates of the mean first exit time from a ball for the [alpha]-stable Ornstein-Uhlenbeck processes

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  • Jakubowski, Tomasz

Abstract

We consider the [alpha]-stable Ornstein-Uhlenbeck process as a solution of the Langevin equation where the Brownian motion is replaced by an isotropic [alpha]-stable process. We give sharp estimates for the expectation of the first exit time from the center of a ball B(x,r) for all and r>0. We compare these results with the case of the Ornstein-Uhlenbeck diffusion process.

Suggested Citation

  • Jakubowski, Tomasz, 2007. "The estimates of the mean first exit time from a ball for the [alpha]-stable Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1540-1560, October.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:10:p:1540-1560
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    References listed on IDEAS

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    1. Samorodnitsky, G. & Grigoriu, M., 2003. "Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 69-97, May.
    2. Imkeller, P. & Pavlyukevich, I., 2006. "First exit times of SDEs driven by stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 611-642, April.
    3. Patie, Pierre, 2005. "On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 593-607, April.
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