MEAN VARIANCE AND SKEWNESS OF THE FIRST PASSAGE TIME FOR THE ORNSTEIN-UHLENBECK PROCESS

Mean, variance, and skewness of the first passage time distribution for a normalized Ornstein-Uhlenbeck process and for time-independent thresholds are obtained for a set of preassigned initial values. This is done to complement the statistical tables by Keilson and Ross (1971) and in order to allow for ranges of the parameters of neurobiological interest.

[1]  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.

[2]  P. Johannesma,et al.  Diffusion Models for the Stochastic Activity of Neurons , 1968 .

[3]  L. Ricciardi,et al.  FIRST PASSAGE TIME PROBLEMS AND SOME RELATED COMPUTATIONAL METHODS , 1982 .

[4]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[5]  M. Kac.  Random Walk and the Theory of Brownian Motion , 1947 .

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

[7]  R. Anderssen,et al.  On the numerical solution of Brownian motion processes , 1973, Journal of Applied Probability.

[8]  D. R. Smith,et al.  Analysis of the exponential decay model of the neuron showing frequency threshold effects. , 1969, The Bulletin of mathematical biophysics.

[9]  P. Mazur.  On the theory of brownian motion , 1959 .

[10]  J. Hammersley,et al.  Diffusion Processes and Related Topics in Biology , 1977 .

[11]  H. E. Daniels.  The minimum of a stationary Markov process superimposed on a U-shaped trend , 1969 .

[12]  M. Thomas.  Some mean first-passage time approximations for the Ornstein-Uhlenbeck process , 1975, Journal of Applied Probability.

[13]  Donald H. Perkel,et al.  Solutions for a stochastic model of neuronal spike production , 1970 .

[14]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

[15]  J. Durbin.  Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test , 1971, Journal of Applied Probability.

[16]  J. Doob,et al.  The Brownian Movement and Stochastic Equations , 1942 .