First passage time distribution of a Wiener process with drift concerning two elastic barriers

1996 ◽  
Vol 33 (1) ◽  
pp. 164-175 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Explicit Expression ◽  
Wiener Process ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Special Choice ◽  
First Passage ◽  
Special Cases ◽  
Reflecting Barriers

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of elastic boundaries and a fixed start point. An explicit expression is obtained for the first passage density. The cases with pure absorbing and/or reflecting barriers arise for a special choice of a parameter constellation. These special cases are compared with results in Darling and Siegert [5] and Sweet and Hardin [15].

First passage time distribution of a Wiener process with drift concerning two elastic barriers

1996 ◽  
Vol 33 (01) ◽  
pp. 164-175 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Explicit Expression ◽  
Wiener Process ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Special Choice ◽  
First Passage ◽  
Special Cases ◽  
Reflecting Barriers

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of elastic boundaries and a fixed start point. An explicit expression is obtained for the first passage density. The cases with pure absorbing and/or reflecting barriers arise for a special choice of a parameter constellation. These special cases are compared with results in Darling and Siegert [5] and Sweet and Hardin [15].

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (04) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

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

1977 ◽  
Vol 14 (4) ◽  
pp. 850-856 ◽  
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.

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

1977 ◽  
Vol 14 (04) ◽  
pp. 850-856 ◽  
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.

Non-Markovian Fokker-Planck equation: Solutions and first passage time distribution

2006 ◽  
Vol 73 (3) ◽  
Author(s):  
P. C. Assis ◽  
R. P. de Souza ◽  
P. C. da Silva ◽  
L. R. da Silva ◽  
L. S. Lucena ◽  
...  
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Fokker Planck Equation ◽  
Fokker Planck

Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

2011 ◽  
Vol 52 (8) ◽  
pp. 083301 ◽  
Author(s):  
A. T. Silva ◽  
E. K. Lenzi ◽  
L. R. Evangelista ◽  
M. K. Lenzi ◽  
H. V. Ribeiro ◽  
...  
Keyword(s):  
Anomalous Diffusion ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Fokker Planck Equation ◽  
Fokker Planck

Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

1987 ◽  
Vol 1 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Mark Brown ◽  
Yi-Shi Shao
Keyword(s):  
Markov Processes ◽  
Time Distribution ◽  
Infinitesimal Generator ◽  
Spectral Representation ◽  
First Passage Time ◽  
Passage Time ◽  
Spectral Approach ◽  
Generator Matrix ◽  
Eigenvalues And Eigenvectors ◽  
First Passage

The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.

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