A Probabilistic Theory of Random Maps

2005 ◽  
Author(s):  
Ozer Elbeyli ◽  
J. Q. Sun
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
Probabilistic Theory ◽  
Kolmogorov Equations ◽  
Random Maps ◽  
Continuous State ◽  
Time Problem ◽  
Fpk Equation ◽  
The Moment ◽  
First Passage Time Problem

We present a probabilistic theory of random maps with discrete time and continuous state. The forward and backward Kolmogorov equations as well as the FPK equation governing the evolution of the probability density function of the system are derived. The moment equations, the reliability and first passage time problem are studied. The present work compliments the existing theory of continuous time stochastic processes.

Some remarks on the Rayleigh process

1986 ◽  
Vol 23 (2) ◽  
pp. 398-408 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi ◽  
L. Sacerdote
Keyword(s):  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Time Problem ◽  
The Moment ◽  
First Passage Time Problem ◽  
Rayleigh Process ◽  
Absorption Condition

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.

Some remarks on the Rayleigh process

1986 ◽  
Vol 23 (02) ◽  
pp. 398-408 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi ◽  
L. Sacerdote
Keyword(s):  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Time Problem ◽  
The Moment ◽  
First Passage Time Problem ◽  
Rayleigh Process ◽  
Absorption Condition

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.

scholarly journals Non-radial functions, nonlocal operators and Markov processes over p-adic numbers

2019 ◽  
Vol 24 (2) ◽  
pp. 381-406 ◽  
Author(s):  
Leonardo Fabio Chacón-Cortés ◽  
Oscar Francisco Casas-Sánchez
Keyword(s):  
Markov Processes ◽  
First Passage Time ◽  
Parabolic Type ◽  
Passage Time ◽  
Fundamental Solutions ◽  
Nonlocal Operators ◽  
Transition Functions ◽  
Time Problem ◽  
The Cauchy Problem ◽  
First Passage Time Problem

The main goal of this article is to study a new class of nonlocal operators and the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated with them. The fundamental solutions of these equations are transition functions of Markov processes on an n-dimensional vector space over the p-adic numbers. We also study some properties of these Markov processes, including the first passage time problem.

scholarly journals An approximation for the inverse first passage time problem

2011 ◽  
Vol 43 (01) ◽  
pp. 264-275 ◽  
Author(s):  
Jing-Sheng Song ◽  
Paul Zipkin
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Problem ◽  
First Passage Time Problem

We propose an approximation for the inverse first passage time problem. It is similar in spirit and method to the tangent approximation for the original first passage time problem. We provide evidence that the technique is quite accurate in many cases. We also identify some cases where the approximation performs poorly.

First‐Passage Time Problem

1970 ◽  
Vol 47 (1B) ◽  
pp. 393-394 ◽  
Author(s):  
Jann‐Nan Yang ◽  
Masanobu Shinozuka
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Problem ◽  
First Passage Time Problem

General models for r-molecular reactions

1969 ◽  
Vol 6 (1) ◽  
pp. 74-87 ◽  
Author(s):  
G.M. Tallis ◽  
R.T. Leslie
Keyword(s):  
Stochastic Models ◽  
Diffusion Theory ◽  
First Passage Time ◽  
Passage Time ◽  
Theory Approach ◽  
Deterministic Theory ◽  
First Order ◽  
Time Problem ◽  
Reaction Orders ◽  
First Passage Time Problem

In the present paper we consider the r-molecular reversible reaction rA⇌B from several viewpoints. The deterministic theory for integral reaction orders is considered first and is subsequently extended to cover the case of fractional order reactions. Stochastic models are then proposed, the analyses being carried through by spectral methods and, in the case of first order reactions, the first passage time problem is also examined. Finally, we use a diffusion theory approach to the problem to obtain results which are valid for a large number of molecules.

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