Optimum Test Procedures for the Mean of First Passage Time Distribution in Brownian Motion with Positive Drift (Inverse Gaussian Distribution)

Technometrics ◽  
1976 ◽  
Vol 18 (2) ◽  
pp. 189-193 ◽  
Author(s):  
Raj S. Chhikara ◽  
J. Leroy Folks
Keyword(s):  
Brownian Motion ◽  
Gaussian Distribution ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
Inverse Gaussian Distribution ◽  
Inverse Gaussian ◽  
Test Procedures ◽  
First Passage ◽  
The Mean

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

1975 ◽  
Vol 12 (3) ◽  
pp. 600-604 ◽  
Author(s):  
Marlin U. Thomas
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Accurate Method ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Numerical Comparisons ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

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.

scholarly journals First Passage Time of Skew Brownian Motion

2012 ◽  
Vol 49 (3) ◽  
pp. 685-696 ◽  
Author(s):  
Thilanka Appuhamillage ◽  
Daniel Sheldon
Keyword(s):  
Brownian Motion ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Skew Brownian Motion

Nearly fifty years after the introduction of skew Brownian motion by Itô and McKean (1963), the first passage time distribution remains unknown. In this paper we first generalize results of Pitman and Yor (2011) and Csáki and Hu (2004) to derive formulae for the distribution of ranked excursion heights of skew Brownian motion, and then use these results to derive the first passage time distribution.

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

Polymers ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 251 ◽  
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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