Journal of Applied Probability

A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process

Peter J. Thomas

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Abstract

We prove that the first passage time density ρ(t) for an Ornstein-Uhlenbeck process X(t) obeying dX = -β Xdt + σdW to reach a fixed threshold θ from a suprathreshold initial condition x0 > θ > 0 has a lower bound of the form ρ(t) > kexp[-pet] for positive constants k and p for times t exceeding some positive value u. We obtain explicit expressions for k, p, and u in 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.

Article information

Source
J. Appl. Probab. Volume 48, Number 2 (2011), 420-434.

Dates
First available in Project Euclid: 21 June 2011

Permanent link to this document
http://projecteuclid.org/euclid.jap/1308662636

Digital Object Identifier
doi:10.1239/jap/1308662636

Zentralblatt MATH identifier
05918592

Mathematical Reviews number (MathSciNet)
MR2840308

Subjects
Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Secondary: 92C20: Neural biology

Keywords
Leaky integrate and fire neuron Ornstein-Uhlenbeck process reliability synchronization neural model lower bound

Citation

Thomas, Peter J. A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process. Journal of Applied Probability 48 (2011), no. 2, 420--434. doi:10.1239/jap/1308662636. http://projecteuclid.org/euclid.jap/1308662636.


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