The first passage time density of Ornstein-Uhlenbeck process with continuous and impulsive excitations

被引:2
作者
Chen, Zi-Yi [1 ,2 ]
Kang, Yan-Mei [1 ]
机构
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Dept Appl Math, Xian 710049, Peoples R China
[2] Cornell Univ, Dept Stat Sci, Ithaca, NY 14853 USA
关键词
First passage time; Ornstein-Uhlenbeck process; Coherent impulse excitation; Alpha function approximation; Convergence in probability; STOCHASTIC RESONANCE; INTEGRAL-EQUATION; MODEL; NEURONS;
D O I
10.1016/j.chaos.2016.05.018
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The first passage time of the Ornstein Uhlenbeck process plays a prototype role in various noise-induced escape problems. In order to calculate the first passage time density of the Ornstein Uhlenbeck process modulated by continuous and impulsive periodic excitations using the second kind Volterra integral equation method, we adopt an approximation scheme of approaching Dirac delta function by alpha function to transform the involved discontinuous dynamical threshold into a smooth one. It is proven that the first passage time of the approximate model converges to the first passage time of the original model in probability as the approximation exponent alpha tends to infinity. For given parameters, our numerical realizations further demonstrate that good approximation effect can be achieved when the approximation exponent alpha is 10. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码:214 / 220
页数:7
相关论文
共 37 条
[21]   Relaxation rate and stochastic resonance of a single-mode nonlinear optical system [J].
Kang, YM ;
Xu, JX ;
Xie, Y .
ACTA PHYSICA SINICA, 2003, 52 (11) :2712-2717
[22]   Impulsive Vaccination SEIR Model with Nonlinear Incidence Rate and Time Delay [J].
Li, Dongmei ;
Gui, Chunyu ;
Luo, Xuefeng .
MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
[23]   SIR-SVS epidemic models with continuous and impulsive vaccination strategies [J].
Li, Jianquan ;
Yang, Yali .
JOURNAL OF THEORETICAL BIOLOGY, 2011, 280 (01) :108-116
[24]   On a Gaussian neuronal field model [J].
Lu, Wenlian ;
Rossoni, Enrico ;
Feng, Jianfeng .
NEUROIMAGE, 2010, 52 (03) :913-933
[25]   Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data [J].
Mullowney, Paul ;
Iyengar, Satish .
JOURNAL OF COMPUTATIONAL NEUROSCIENCE, 2008, 24 (02) :179-194
[26]   Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model [J].
Paninski, Liam ;
Haith, Adrian ;
Szirtes, Gabor .
JOURNAL OF COMPUTATIONAL NEUROSCIENCE, 2008, 24 (01) :69-79
[27]  
Paulwels EJ, 1987, J APPL PROBAB, V24, P360
[28]   Stochastic resonance in a model neuron with reset [J].
Plesser, HE ;
Tanaka, S .
PHYSICS LETTERS A, 1997, 225 (4-6) :228-234
[29]   Reaction rate theory: What it was, where is it today, and where is it going? [J].
Pollak, E ;
Talkner, P .
CHAOS, 2005, 15 (02)
[30]   Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive [J].
Richardson, Magnus J. E. .
PHYSICAL REVIEW E, 2007, 76 (02)