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June 2011 A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process
Peter J. Thomas
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J. Appl. Probab. 48(2): 420-434 (June 2011). DOI: 10.1239/jap/1308662636

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.

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Peter J. Thomas. "A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process." J. Appl. Probab. 48 (2) 420 - 434, June 2011. https://doi.org/10.1239/jap/1308662636

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1242.60086
MathSciNet: MR2840308
Digital Object Identifier: 10.1239/jap/1308662636

Subjects:
Primary: 60J70
Secondary: 92C20

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 2 • June 2011
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