论文信息 - The Statistics Of Spikes Trains For Some Simple Types Of Neuron Models

The Statistics Of Spikes Trains For Some Simple Types Of Neuron Models

Ce rapport de recherche decrit les resultats preliminaires d'un travail visant a caracteriser les distributions statistiques des trains de spikes, pour certains modeles de neurones couramment utilises, en presence de bruit stochastique et avec des entrees deterministes. Le principal angle d'attaque du probleme est l'utilisation du calcul stochastique et la representations des martingales (locales) comme un mouvement brownien via un changement de l'echelle de temps.

[1] Volker Strassen,et al. Almost sure behavior of sums of independent random variables and martingales , 1967 .

[2] D. W. Stroock,et al. Multidimensional Diffusion Processes , 1979 .

[3] H. Risken. The Fokker-Planck equation : methods of solution and applications , 1985 .

[4] P. Groeneboom. Brownian motion with a parabolic drift and airy functions , 1989 .

[5] J. Durbin. THE FIRST-PASSAGE DENSITY OF A CONTINUOUS GAUSSIAN PROCESS , 1985 .

[6] Shunsuke Sato,et al. First-passage-time density and moments of the Ornstein-Uhlenbeck process , 1988 .

[7] Henry C. Tuckwell,et al. Introduction to theoretical neurobiology , 1988 .

[8] N. Brunel,et al. Firing frequency of leaky intergrate-and-fire neurons with synaptic current dynamics. , 1998, Journal of theoretical biology.

[9] P. Patie. On some First Passage Time Problems Motivated by Financial Applications , 2004 .

[10] Wulfram Gerstner,et al. Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. , 2005, Journal of neurophysiology.

[11] Eugene M. Izhikevich,et al. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .