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A Recursion Formula for the Moments of the First Passage Time of the Ornstein-Uhlenbeck Process

Part of: Markov processes Special processes

Published online by Cambridge University Press:  30 January 2018

Dirk Veestraeten
Dirk Veestraeten*
Affiliation:
University of Amsterdam
*
∗ Postal address: Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018WB Amsterdam, The Netherlands. Email address: [email protected]
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Abstract

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In this paper we use the Siegert formula to derive alternative expressions for the moments of the first passage time of the Ornstein-Uhlenbeck process through a constant threshold. The expression for the nth moment is recursively linked to the lower-order moments and consists of only n terms. These compact expressions can substantially facilitate (numerical) applications also for higher-order moments.

Keywords

Ornstein-Uhlenbeck processfirst passage timemomentsconstant threshold

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 595 - 601
Copyright
© Applied Probability Trust 

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