Fractional nonlinear diffusion equation and first passage time

2008 ◽  
Vol 387 (4) ◽  
pp. 764-772 ◽  
Author(s):  
Jun Wang ◽  
Wen-Jun Zhang ◽  
Jin-Rong Liang ◽  
Jian-Bin Xiao ◽  
Fu-Yao Ren
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
First Passage Time ◽  
Passage Time ◽  
Nonlinear Diffusion Equation ◽  
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.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap
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