Document Zbl 0525.92006

Ricciardi, L. M.; Sacerdote, L.; Sato, S.

Diffusion approximation and first passage time problem for a model neuron. II. Outline of a computation method. (English) Zbl 0525.92006

Math. Biosci. 64, 29-44 (1983).

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MSC:

92Cxx	Physiological, cellular and medical topics
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
92-08	Computational methods for problems pertaining to biology

Keywords:

first passage time problem; model neuron; Brownian bridge; nonstationary effects; diffusion approximations; neurobiology; transformation technique

Citations:

Zbl 0224.92008; Zbl 0225.60037

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References:

[1]	Capocelli, R. M.; Ricciardi, L. M., Diffusion approximation and first passage time problem for a model neuron, Kybernetik, 8, 214-223 (1971) · Zbl 0224.92008
[2]	Cerbone, G.; Ricciardi, L. M.; Sacerdote, L., Mean variance and skewness of the first passage time for the Ornstein-Uhlenbeck process, Cybernetics and Systems, 12, 395-429 (1981) · Zbl 0513.60078
[3]	Daniels, H. E., The minimum of a stationary Markov process superimposed on a U-shaped trend, J. Appl. Probab., 6, 399-408 (1969) · Zbl 0209.19702
[4]	DeGriffi, E. M.; Favella, L., On a weakly singular Volterra integral equation, Calcolo, Vol. XVIII, 153-195 (1981) · Zbl 0517.65095
[5]	Durbin, J., Boundary crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test, J. Appl. Probab., 8, 431-453 (1971) · Zbl 0225.60037
[6]	Favella, L.; Reineri, M. T.; Ricciardi, L. M.; Sacerdote, L., First passage time problems and related computational methods, Cybernetics and Systems, 13, 95-128 (1982) · Zbl 0499.60087
[7]	Gerstein, G. L.; Mandelbrot, B., Random walk models for the spike activity for a single neuron, Biophys. J., 4, 41-67 (1964)
[8]	Hearth, R. A., A tandem random walk model for psychological discrimination, British J. Math. Statist. Psych., 34, 76-92 (1981) · Zbl 0471.92023
[9]	Ratcliff, R., A note on modeling accumulation of information when the rate of accumulation changes with time, J. Math. Psych., 21, 178-184 (1980) · Zbl 0435.92029
[10]	Ricciardi, L. M., On the transformation of diffusion processes into the Wiener process, J. Math. Anal. Appl., 54, 185-199 (1976) · Zbl 0361.60043
[11]	Ricciardi, L. M., Diffusion Processes and Related Topics in Biology, (Lecture Notes in Biomathematics, Vol. 14 (1977), Springer: Springer Berlin) · Zbl 0575.92009
[12]	Ricciardi, L. M.; Sacerdote, L., The Ornstein-Uhlenbeck process as a model for neuronal activity, I. Mean and variance of the firing time, Biol. Cybernet., 35, 1-9 (1979) · Zbl 0414.92010
[14]	Sato, S., On the moments of the firing interval of the diffusion approximated model neuron, Math. Biosci., 39, 53-70 (1978) · Zbl 0391.92005

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