A note on the first-passage problem and VanMarcke's approximation - short communication

Phaedon-Stelios Koutsourelakis

doi:10.1016/j.probengmech.2006.05.003

A note on the first-passage problem and VanMarcke's approximation - short communication

Phaedon-Stelios Koutsourelakis

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 195 1; 81:617-23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215-20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process. (C) 2006 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	22-26
Number of pages	5
Journal	Probabilistic Engineering Mechanics
Volume	22
Issue number	1
DOIs	https://doi.org/10.1016/j.probengmech.2006.05.003
Publication status	Published - Jan 2007

Keywords

first-passage problem
binary process
Markov process

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10.1016/j.probengmech.2006.05.003

Cite this

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title = "A note on the first-passage problem and VanMarcke's approximation - short communication",

abstract = "Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 195 1; 81:617-23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215-20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process. (C) 2006 Elsevier Ltd. All rights reserved.",

keywords = "first-passage problem, binary process, Markov process",

author = "Phaedon-Stelios Koutsourelakis",

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doi = "10.1016/j.probengmech.2006.05.003",

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AU - Koutsourelakis, Phaedon-Stelios

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AB - Given a scalar, stationary, Markov process, this short communication presents a closed-form solution for the first-passage problem for a fixed threshold b. The derivation is based on binary processes and the general formula of Siegert [Siegert AJF. On the first-passage time probability problem. Physical Review 195 1; 81:617-23]. The relation for the probability density function of the first-passage time is identical to the commonly used formula that was derived by VanMarcke [VanMarcke E. On the distribution of the first-passage time for normal stationary random processes. Journal of Applied Mechanics ASME 1975; 42:215-20] for Gaussian processes. The present derivation is based on more general conditions and reveals the criteria for the validity of the approximation. Properties of binary processes are also used to derive a hierarchy of upper bounds for any scalar process. (C) 2006 Elsevier Ltd. All rights reserved.

KW - first-passage problem

KW - binary process

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DO - 10.1016/j.probengmech.2006.05.003

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EP - 26

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

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ER -

A note on the first-passage problem and VanMarcke's approximation - short communication

Abstract

Keywords

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