Small noise asymptotics and first passage times of integrated Ornstein-Uhlenbeck processes driven by \(\alpha\)-stable Lévy processes

DOI10.3150/12-BEJ485zbMath1309.60059arXiv1205.6116MaRDI QIDQ2444668

Robert Hintze, Ilya Pavlyukevitch

Publication date: 10 April 2014

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.6116

zbMATH Keywords

first passage timessmall noise asymptoticsintegrated Ornstein-Uhlenbeck processes\(\alpha\)-stable Lévy processesabsolutely continuous approximationsSkorokhod M1-topology

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stable stochastic processes (60G52)

Related Items (7)

Approximations of Lévy processes by integrated fast oscillating Ornstein–Uhlenbeck processes ⋮ Random acceleration process on finite intervals under stochastic restarting ⋮ Strong approximation rate for Wiener process by fast oscillating integrated Ornstein-Uhlenbeck processes ⋮ A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale ⋮ A Wong-Zakai approximation for random slow manifolds with application to parameter estimation ⋮ Non-Standard Skorokhod Convergence of Lévy-Driven Convolution Integrals in Hilbert Spaces ⋮ Non-Gaussian limit theorem for non-linear Langevin equations driven by Lévy noise

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