First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval

2015 ◽  
Vol 433 ◽  
pp. 279-290 ◽  
Author(s):  
Gang Guo ◽  
Bin Chen ◽  
Xinjun Zhao ◽  
Fang Zhao ◽  
Quanmin Wang
Keyword(s):  
Diffusion Equation ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Infinite Interval ◽  
First Passage

On the inverse of the first passage time probability problem

1972 ◽  
Vol 9 (2) ◽  
pp. 270-287 ◽  
Author(s):  
R. M. Capocelli ◽  
L. M. Ricciardi
Keyword(s):  
Inverse Problem ◽  
Probability Density Function ◽  
Diffusion Equation ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Homogeneous Markov Process ◽  
Markov Diffusion ◽  
Singular Diffusion

Since the pioneering work of Siegert (1951), the problem of determining the first passage time distribution for a preassigned continuous and time homogeneous Markov process described by a diffusion equation has been deeply analyzed and satisfactorily solved. Here we discuss the “inverse problem” — of applicative interest — consisting in deciding whether a given function can be considered as the first passage time probability density function for some continuous and homogeneous Markov diffusion process. A constructive criterion is proposed, and some examples are provided. One of these leads to a singular diffusion equation representing a dynamical model for the genesis of the lognormal distribution.

On the inverse of the first passage time probability problem

1972 ◽  
Vol 9 (02) ◽  
pp. 270-287 ◽  
Author(s):  
R. M. Capocelli ◽  
L. M. Ricciardi
Keyword(s):  
Inverse Problem ◽  
Probability Density Function ◽  
Diffusion Equation ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Homogeneous Markov Process ◽  
Markov Diffusion ◽  
Singular Diffusion

Since the pioneering work of Siegert (1951), the problem of determining the first passage time distribution for a preassigned continuous and time homogeneous Markov process described by a diffusion equation has been deeply analyzed and satisfactorily solved. Here we discuss the “inverse problem” — of applicative interest — consisting in deciding whether a given function can be considered as the first passage time probability density function for some continuous and homogeneous Markov diffusion process. A constructive criterion is proposed, and some examples are provided. One of these leads to a singular diffusion equation representing a dynamical model for the genesis of the lognormal distribution.

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.

scholarly journals On the First Passage Time Distribution for a Class of Markov Chains

1983 ◽  
Vol 11 (4) ◽  
pp. 1000-1008 ◽  
Author(s):  
Mark Brown ◽  
Narasinga R. Chaganty
Keyword(s):  
Markov Chains ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage

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.

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