Diffusion Models for the Stochastic Activity of Neurons

The activity of a neuron, subjected to an input of many small excitatory and inhibitory pulses, is considered. Diffusion equations for transition probabilities and first passage times are derived.

[1]  R. Stein.  A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY. , 1965, Biophysical journal.

[2]  Alexander Joseph.  Book reviewDischarge patterns of single fibers in the cat's auditory nerve: Nelson Yuan-Sheng Kiang, with the assistance of Takeshi Watanabe, Eleanor C. Thomas and Louise F. Clark: Research Monograph no. 35. Cambridge, Mass., The M.I.T. Press, 1965 , 1967 .

[3]  Ian Graham Cumming.  Computing aspects of problems in non-linear prediction and filtering , 1967 .

[4]  C. Stevens.  ArticlesLetters to the Editor , 1964 .

[5]  Motoo Kimura,et al.  Diffusion models in population genetics , 1964, Journal of Applied Probability.

[6]  G. P. Moore,et al.  Statistical analysis and functional interpretation of neuronal spike data. , 1966, Annual review of physiology.

[7]  B Gluss,et al.  A model for neuron firing with exponential decay of potential resulting in diffusion equations for probability density. , 1967, The Bulletin of mathematical biophysics.

[8]  M. Hoopen,et al.  Probabilistic firing of neurons considered as a first passage problem. , 1966, Biophysical journal.

[9]  R. L. Stratonovich,et al.  Topics in the theory of random noise , 1967 .

[10]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[11]  G. Poggio,et al.  TIME SERIES ANALYSIS OF IMPULSE SEQUENCES OF THALAMIC SOMATIC SENSORY NEURONS. , 1964, Journal of neurophysiology.

[12]  H. D. Miller,et al.  The Theory Of Stochastic Processes , 1977, The Mathematical Gazette.

[13]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[14]  D. Rasch.  Kimura, M.: Diffusion Models in Populations Genetics. Methuen Monographs on Applied Probability and Statistics. Suppl. Rev. Ser. in Appl. Prob. Vol. 2. Methuen & Co LTD, London 1964, 57 S., 10 Abb., 1 Tab., Preis 8 s 6 d , 1969 .

[15]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[16]  D. Middleton.  An Introduction to Statistical Communication Theory , 1960 .

[17]  R. Stein.  Some models of neuronal variability. , 1967, Biophysical journal.

[18]  B. Mandelbrot,et al.  RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. , 1964, Biophysical journal.

[19]  R. E. Olsen,et al.  Dynamic statistics of crayfish caudal photoreceptors. , 1967, Biophysical journal.

[20]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[21]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .