Hitting Times with Respect to Time-Dependent Barriers

2016 ◽  
Author(s):  
Daniel Berger
Keyword(s):  
Time Dependent ◽  
Hitting Times

scholarly journals Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries

2014 ◽  
Vol 46 (01) ◽  
pp. 186-202 ◽  
Author(s):  
Laura Sacerdote ◽  
Ottavia Telve ◽  
Cristina Zucca
Keyword(s):  
Diffusion Process ◽  
Joint Distribution ◽  
Continuous Functions ◽  
Time Dependent ◽  
Hitting Times ◽  
Convergence Properties ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
First Hitting Times

Consider a one-dimensional diffusion process on the diffusion interval I originated in x 0 ∈ I. Let a(t) and b(t) be two continuous functions of t, t > t 0, with bounded derivatives, a(t) < b(t), and a(t), b(t) ∈ I, for all t > t 0. We study the joint distribution of the two random variables T a and T b , the first hitting times of the diffusion process through the two boundaries a(t) and b(t), respectively. We express the joint distribution of T a and T b in terms of ℙ(T a < t, T a < T b ) and ℙ(T b < t, T a > T b ), and we determine a system of integral equations verified by these last probabilities. We propose a numerical algorithm to solve this system and we prove its convergence properties. Examples and modeling motivation for this study are also discussed.

scholarly journals Joint Densities of First Hitting Times of a Diffusion Process Through Two Time-Dependent Boundaries

2014 ◽  
Vol 46 (1) ◽  
pp. 186-202 ◽  
Author(s):  
Laura Sacerdote ◽  
Ottavia Telve ◽  
Cristina Zucca
Keyword(s):  
Diffusion Process ◽  
Joint Distribution ◽  
Continuous Functions ◽  
Time Dependent ◽  
Hitting Times ◽  
Convergence Properties ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
First Hitting Times

Consider a one-dimensional diffusion process on the diffusion interval I originated in x0 ∈ I. Let a(t) and b(t) be two continuous functions of t, t > t0, with bounded derivatives, a(t) < b(t), and a(t), b(t) ∈ I, for all t > t0. We study the joint distribution of the two random variables Ta and Tb, the first hitting times of the diffusion process through the two boundaries a(t) and b(t), respectively. We express the joint distribution of Ta and Tb in terms of ℙ(Ta < t, Ta < Tb) and ℙ(Tb < t, Ta > Tb), and we determine a system of integral equations verified by these last probabilities. We propose a numerical algorithm to solve this system and we prove its convergence properties. Examples and modeling motivation for this study are also discussed.

TIME-DEPENDENT PHENOMENA CAUSED BY THE EC DECAY IN Co2+ [Fe(CN)6]3-

1980 ◽  
Vol 41 (C1) ◽  
pp. C1-239-C1-240 ◽  
Author(s):  
Takayuki Kobayashi ◽  
Tetsuo Kitahara
Keyword(s):  
Time Dependent
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