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1 results

  • A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

  • Part of
  • Peter J. Thomas
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 2 / June 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 420-434
    Print publication:
    June 2011
    • Article
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  • 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[-pe6βt] 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.