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 First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (1) ◽  
pp. 175-184 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

scholarly journals First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (01) ◽  
pp. 175-184
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a &gt; 0 or −b &lt; 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

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

Properties of noninteger moments in a first passage time problem

1989 ◽  
Vol 55 (1-2) ◽  
pp. 435-439 ◽  
Author(s):  
George H. Weiss ◽  
Shlomo Havlin ◽  
Ofer Matan
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Problem ◽  
First Passage Time Problem
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