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On first passage times of sticky reflecting diffusion processes with double exponential jumps

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  04 May 2020

Shiyu Song Open the ORCID record for Shiyu Song [Opens in a new window]  and
Yongjin Wang
Shiyu Song*
Affiliation:
Tianjin University
Yongjin Wang*
Affiliation:
Nankai University
*
*Postal address: School of Mathematics, Tianjin University, Tianjin, 300354, China. Email address: shiyu.song@tju.edu.cn
**Postal address: School of Business, Nankai University, Tianjin 300071, China.
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Abstract

We explore the first passage problem for sticky reflecting diffusion processes with double exponential jumps. The joint Laplace transform of the first passage time to an upper level and the corresponding overshoot is studied. In particular, explicit solutions are presented when the diffusion part is driven by a drifted Brownian motion and by an Ornstein–Uhlenbeck process.

Keywords

First passage timesticky reflecting processesdouble exponential jumps

MSC classification

Primary: 60G55: Point processes
Secondary: 60J60: Diffusion processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 1 , March 2020 , pp. 221 - 236
Copyright
© Applied Probability Trust 2020

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