Some mean first-passage time approximations for the Ornstein-Uhlenbeck process

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.

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On the first passage time distribution of an Ornstein–Uhlenbeck process

Quantitative Finance ◽

10.1080/14697680903373684 ◽

2010 ◽

Vol 10 (9) ◽

pp. 957-960 ◽

Cited By ~ 21

Author(s):

Chuang Yi

Keyword(s):

Time Distribution ◽

First Passage Time ◽

Passage Time ◽

First Passage ◽

Uhlenbeck Process ◽

Ornstein Uhlenbeck Process

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Evaluation of the first-passage time probability to a square root boundary for the Wiener process

Journal of Applied Probability ◽

10.2307/3213358 ◽

1977 ◽

Vol 14 (4) ◽

pp. 850-856 ◽

Cited By ~ 35

Author(s):

Shunsuke Sato

Keyword(s):

Wiener Process ◽

Time Distribution ◽

First Passage Time ◽

Passage Time ◽

Square Root ◽

First Passage ◽

Uhlenbeck Process ◽

Ornstein Uhlenbeck Process ◽

Asymptotic Evaluation

This paper gives an asymptotic evaluation of the probability that the Wiener path first crosses a square root boundary. The result is applied to estimate the moments of the first-passage time distribution of the Ornstein–Uhlenbeck process to a constant boundary.

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Evaluation of the first-passage time probability to a square root boundary for the Wiener process

Journal of Applied Probability ◽

10.1017/s0021900200105388 ◽

1977 ◽

Vol 14 (04) ◽

pp. 850-856 ◽

Cited By ~ 9

Author(s):

Shunsuke Sato

Keyword(s):

Wiener Process ◽

Time Distribution ◽

First Passage Time ◽

Passage Time ◽

Square Root ◽

First Passage ◽

Uhlenbeck Process ◽

Ornstein Uhlenbeck Process ◽

Asymptotic Evaluation

This paper gives an asymptotic evaluation of the probability that the Wiener path first crosses a square root boundary. The result is applied to estimate the moments of the first-passage time distribution of the Ornstein–Uhlenbeck process to a constant boundary.

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First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time

Scientific Reports ◽

10.1038/srep20349 ◽

2016 ◽

Vol 6 (1) ◽

Cited By ~ 56

Author(s):

Aljaž Godec ◽

Ralf Metzler

Keyword(s):

Time Distribution ◽

First Passage Time ◽

Passage Time ◽

Mean First Passage Time ◽

First Passage ◽

The Mean

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Polymer Translocation Across a Corrugated Channel: Fick–Jacobs Approximation Extended Beyond the Mean First-Passage Time

Polymers ◽

10.3390/polym11020251 ◽

2019 ◽

Vol 11 (2) ◽

pp. 251 ◽

Cited By ~ 5

Author(s):

Paolo Malgaretti ◽

Gleb Oshanin

Keyword(s):

Time Distribution ◽

First Passage Time ◽

Passage Time ◽

Characteristic Time Scale ◽

Mean First Passage Time ◽

First Passage ◽

Systematic Analysis ◽

Corrugated Channel ◽

The Mean ◽

Polymer Translocation

Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time-scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocation dynamics of a Gaussian polymer in a periodically-corrugated channel using an appropriately generalized Fick–Jacobs approach. Our main aim is to probe an effective broadness of the first-passage time distribution (FPTD), by determining the so-called coefficient of variation γ of the FPTD, defined as the ratio of the standard deviation versus the mean first-passage time (MFPT). We present a systematic analysis of γ as a function of a variety of system’s parameters. We show that γ never significantly drops below 1 and, in fact, can attain very large values, implying that the MFPT alone cannot characterize the first-passage statistics of the translocation process exhaustively well.

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