Closed-form solutions for the first-passage-time problem and neuronal modeling

被引：16

作者：

Buonocore A. ^{[1
]}

Caputo L. ^{[1
]}

D’Onofrio G. ^{[1
]}

Pirozzi E. ^{[1
]}

机构：

[1] Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Complesso Monte S. Angelo, Naples

来源：

Ricerche di Matematica | 2015年 / 64卷 / 2期

关键词：

Asymptotics; Gaussian processes; LIF neuronal models; Numerical approximations;

D O I：

10.1007/s11587-015-0248-6

中图分类号：

学科分类号：

摘要：

The Gauss–Diffusion processes are here considered and some relations between their infinitesimal moments and mean and covariance functions are remarked. The corresponding linear stochastic differential equations are re-written specifying the coefficient functions and highlighting their meanings in theoretical and application contexts. We resort the Doob-transformation of a Gauss–Markov process as a transformed Wiener process and we represent some time-inhomogeneous processes as transformed Ornstein–Uhlenbeck process. The first passage time problem is considered in order to discuss some neuronal models based on Gauss–Diffusion processes. We recall some different approaches to solve the first passage time problem specifying when a closed-form result exists and numerical evaluations are required when the latter is not available. In the contest of neuronal modeling, relations between firing threshold, mean behavior of the neuronal membrane voltage and input currents are given for the existence of a closed-form result useful to describe the firing activity. Finally, we collect in an unified way some models and the corresponding Gauss–Diffusion processes already considered by us in some previous papers. © 2015, Università degli Studi di Napoli Federico II"."

引用

页码：421 / 439

页数：18

共 24 条

[1]

Benda J., Herz A.V.M., A universal model for spike-frequency adaptation, Neural Comput., 15, pp. 2523-2564, (2003)

[2]

Bulsara A.R., Elston T.C., Doering C.R., Lowen S.B., Linderberg K., Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics, Phys. Rev. E, 53, 4, pp. 3958-3969, (2011)

[3]

Burkitt A.N., A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biol. Cybern., 95, pp. 1-19, (2006)

[4]

Buonocore A., Caputo L., Pirozzi E., On the evaluation of firing densities for periodically driven neuron models, Math. Biosci., 214, pp. 122-133, (2008)

[5]

Buonocore A., Caputo L., Pirozzi E., Ricciardi L.M., On a stochastic leaky integrate-and-fire neuronal model, Neural Comput., 22, pp. 2558-2585, (2010)

[6]

Buonocore A., Caputo L., Pirozzi E., Ricciardi L.M., The first passage time problem for gauss-diffusion processes: algorithmic approaches and applications to lif neuronal model, Methodol. Comput. Appl. Prob., 13, pp. 29-57, (2011)

[7]

Buonocore A., Caputo L., Pirozzi E., Carfora M.F., Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons, Math. Biosci. Eng., 11, pp. 189-201, (2014)

[8]

Buonocore A., Caputo L., Nobile A.G., Pirozzi E., Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models, Appl. Math. Comput., 232, pp. 799-809, (2014)

[9]

Buonocore A., Caputo L., Nobile A.G., Pirozzi E., Restricted Ornstein–Uhlenbeck process and applications in neuronal models with periodic input signals, J. Comput. Appl. Math., 285, pp. 59-71, (2015)

[10]

Buonocore A., Caputo L., Nobile A.G., Pirozzi E., Gauss–Markov processes for neuronal models including reversal potentials, Adv. Cogn. Neurodyn. (IV), 11, pp. 299-305, (2015)

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