Gauss-Markov processes in the presence of a reflecting boundary and applications in neuronal models

被引：19
作者：
Buonocore, A. [1 ]
Caputo, L. [1 ]
Nobile, A. G. [2 ]
Pirozzi, E. [1 ]
机构：
[1] Univ Naples Federico II, Dipartimento Matemat & Applicazioni, Naples, Italy
[2] Univ Salerno, Dipartimento Studi & Ric Aziendali Management & I, I-84084 Fisciano, SA, Italy
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 232卷
关键词：
Integrate-and-fire model; Ornstein-Uhlenbeck process; Firing densities; Volterra integral equation; Simulation; 1ST-PASSAGE-TIME PROBABILITY DENSITIES; DIFFUSION; INPUT; RATES;
D O I：
10.1016/j.amc.2014.01.143
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Gauss-Markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined. Furthermore, the first-passage time density through a time-dependent threshold is studied by using analytical, numerical and asymptotic methods. The restricted Gauss-Markov processes are then used to construct inhomogeneous leaky integrate-and-fire stochastic models for single neurons activity in the presence of a reversal hyperpolarization potential and time-varying input signals. (c) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：799 / 809
页数：11
相关论文
共 26 条
[1]  
[Anonymous], 1970, The theory of stochastic processes
[2]  
[Anonymous], 1977, Diffusion processes and related topics on biology
[3]   A NEW INTEGRAL-EQUATION FOR THE EVALUATION OF 1ST-PASSAGE-TIME PROBABILITY DENSITIES [J].
BUONOCORE, A ;
NOBILE, AG ;
RICCIARDI, LM .
ADVANCES IN APPLIED PROBABILITY, 1987, 19 (04) :784-800
[4]   On a Stochastic Leaky Integrate-and-Fire Neuronal Model [J].
Buonocore, A. ;
Caputo, L. ;
Pirozzi, E. ;
Ricciardi, L. M. .
NEURAL COMPUTATION, 2010, 22 (10) :2558-2585
[5]   The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model [J].
Buonocore, Aniello ;
Caputo, Luigia ;
Pirozzi, Enrica ;
Ricciardi, Luigi M. .
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2011, 13 (01) :29-57
[6]   A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties [J].
Burkitt, A. N. .
BIOLOGICAL CYBERNETICS, 2006, 95 (02) :97-112
[7]   On some computational results for single neurons' activity modeling [J].
Di Crescenzo, A ;
Di Nardo, E ;
Nobile, AG ;
Pirozzi, E ;
Ricciardi, LM .
BIOSYSTEMS, 2000, 58 (1-3) :19-26
[8]   A computational approach to first-passage-time problems for Gauss-Markov processes [J].
Di Nardo, E ;
Nobile, AG ;
Pirozzi, E ;
Ricciardi, LM .
ADVANCES IN APPLIED PROBABILITY, 2001, 33 (02) :453-482
[9]   DIFFUSION-APPROXIMATION TO A QUEUING SYSTEM WITH TIME-DEPENDENT ARRIVAL AND SERVICE RATES [J].
DICRESCENZO, A ;
NOBILE, AG .
QUEUEING SYSTEMS, 1995, 19 (1-2) :41-62
[10]  
Dirk P., 2011, Handbook of Monte Carlo Methods, DOI [10.1002/9781118014967, DOI 10.1002/9781118014967]
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