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We prove that the first passage time density $\rho(t)$ for anOrnstein-Uhlenbeck process $X(t)$ obeying $dX=-\beta X dt + \sigma dW$ to reacha fixed threshold $\theta$ from a suprathreshold initial condition$x_0>\theta>0$ has a lower bound of the form $\rho(t)>k \exp\left[-p e^{6\betat}\right]$ for positive constants $k$ and $p$ for times $t$ exceeding somepositive value $u$. We obtain explicit expressions for $k, p$ and $u$ in termsof $\beta$, $\sigma$, $x_0$ and $\theta$, and discuss application of theresults to the synchronization of periodically forced stochastic leakyintegrate-and-fire model neurons.

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