A LOWER BOUND FOR THE FIRST PASSAGE TIME DENSITY OF THE SUPRATHRESHOLD ORNSTEIN-UHLENBECK PROCESS

被引：7

作者：

Thomas, Peter J. ^{[1
]}

机构：

[1] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2011年 / 48卷 / 02期

基金：

美国国家科学基金会;

关键词：

Leaky integrate and fire neuron; Ornstein-Uhlenbeck process; reliability; synchronization; neural model; lower bound; STOCHASTIC PHASE LOCKINGS; 1ST-PASSAGE-TIME DENSITIES; DIFFUSION-PROCESSES; EXPONENTIAL TRENDS; MARKOV-PROCESSES; ADDITIVE NOISE; MODE-LOCKING; OSCILLATOR; NEURONS; RELIABILITY;

D O I：

10.1239/jap/1308662636

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that the first passage time density rho(t) for an Ornstein-Uhlenbeck process X (t) obeying dX = -beta X dt + sigma d W to reach a fixed threshold theta from a suprathreshold initial condition x(0) > theta > 0 has a lower bound of the form rho(t) > k exp[- pe(6 beta t)] 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 beta, sigma, x(0), and theta, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.

引用

页码：420 / 434

页数：15

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