A first passage time distribution for a discrete version of the Ornstein–Uhlenbeck process

2004 ◽  
Vol 37 (12) ◽  
pp. 3759-3767 ◽  
Author(s):  
Hernán Larralde
1977 ◽  
Vol 14 (4) ◽  
pp. 850-856 ◽  
Author(s):  
Shunsuke Sato

This paper gives an asymptotic evaluation of the probability that the Wiener path first crosses a square root boundary. The result is applied to estimate the moments of the first-passage time distribution of the Ornstein–Uhlenbeck process to a constant boundary.


1977 ◽  
Vol 14 (04) ◽  
pp. 850-856 ◽  
Author(s):  
Shunsuke Sato

This paper gives an asymptotic evaluation of the probability that the Wiener path first crosses a square root boundary. The result is applied to estimate the moments of the first-passage time distribution of the Ornstein–Uhlenbeck process to a constant boundary.


1975 ◽  
Vol 12 (3) ◽  
pp. 600-604 ◽  
Author(s):  
Marlin U. Thomas

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.


1975 ◽  
Vol 12 (03) ◽  
pp. 600-604 ◽  
Author(s):  
Marlin U. Thomas

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.


1985 ◽  
Vol 22 (02) ◽  
pp. 360-369 ◽  
Author(s):  
A. G. Nobile ◽  
L. M. Ricciardi ◽  
L. Sacerdote

The asymptotic behaviour of the first-passage-time p.d.f. through a constant boundary for an Ornstein–Uhlenbeck process is investigated for large boundaries. It is shown that an exponential p.d.f. arises, whose mean is the average first-passage time from 0 to the boundary. The proof relies on a new recursive expression of the moments of the first-passage-time p.d.f. The excellent agreement of theoretical and computational results is pointed out. It is also remarked that in many cases the exponential behaviour actually occurs even for small values of time and boundary.


2011 ◽  
Vol 48 (02) ◽  
pp. 420-434 ◽  
Author(s):  
Peter J. Thomas

We prove that the first passage time density ρ(t) for an Ornstein-Uhlenbeck processX(t) obeying dX= -βXdt+ σdWto reach a fixed threshold θ from a suprathreshold initial conditionx0> θ > 0 has a lower bound of the form ρ(t) >kexp[-pe6βt] for positive constantskandpfor timestexceeding some positive valueu. We obtain explicit expressions fork,p, anduin terms of β, σ,x0, and θ, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.


1987 ◽  
Vol 24 (02) ◽  
pp. 355-369
Author(s):  
L. M. Ricciardi ◽  
L. Sacerdote

We show that the transition p.d.f. of the Ornstein–Uhlenbeck process with a reflection condition at an assigned state S is related by integral-type equations to the free transition p.d.f., to the transition p.d.f. in the presence of an absorption condition at S, to the first-passage-time p.d.f. to S and to the probability current. Such equations, which are also useful for computational purposes, yield as an immediate consequence all known closed-form results for Wiener and Ornstein–Uhlenbeck processes.


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