Erratum to: “An inverse first-passage problem for one-dimensional diffusions with random starting point” [Statist. Probab. Lett. 82 (2012) 7–14]

2012 ◽  
Vol 82 (3) ◽  
pp. 705 ◽  
Author(s):  
Mario Abundo
Keyword(s):  
First Passage ◽  
One Dimensional ◽  
Starting Point ◽  
Random Starting Point ◽  
First Passage Problem ◽  
Inverse First Passage Problem

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.

scholarly journals Solution and Analysis of a One-Dimensional First-Passage Problem with a Nonzero Halting Probability

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ken Yamamoto
Keyword(s):  
Moment Generating Function ◽  
Hitting Time ◽  
Gauss Hypergeometric Function ◽  
Time Behavior ◽  
First Passage ◽  
One Dimensional ◽  
Random Walker ◽  
Calculation Technique ◽  
The Right ◽  
First Passage Problem

This paper treats a kind of a one-dimensional first-passage problem, which seeks the probability that a random walker first hits the origin at a specified time. In addition to a usual random walk which hops either rightwards or leftwards, the present paper introduces the “halt” that the walker does not hop with a nonzero probability. The solution to the problem is expressed using a Gauss hypergeometric function. The moment generating function of the hitting time is also calculated, and a calculation technique of the moments is developed. The author derives the long-time behavior of the hitting-time distribution, which exhibits power-law behavior if the walker hops to the right and left with equal probability.

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.

scholarly journals Analysis of an Inverse First Passage Problem from Risk Management

2006 ◽  
Vol 38 (3) ◽  
pp. 845-873 ◽  
Author(s):  
Lan Cheng ◽  
Xinfu Chen ◽  
John Chadam ◽  
David Saunders
Keyword(s):  
Risk Management ◽  
First Passage ◽  
First Passage Problem ◽  
Inverse First Passage Problem
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