Accession Number : AD0604005

Title :   PARTIAL DIFFERENTIAL EQUATIONS FOR DENSITIES OF RANDOM PROCESSES,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS CRUFT LAB

Personal Author(s) : Fine,Terrence

Report Date : 04 MAY 1964

Pagination or Media Count : 12

Abstract : The Fokker-Planck-Kolmogorov (FPK) equation appears to be of wider applicability than is commonly realized. It is proved that the density functions for a wider class of vector random processes than just the Markov processes satisfy the FPK equation. Furthermore, an analogous derivation will yield a different partial differential equation applicable to multivariate densities for scalar random processes. The central technique is the evaluation of time derivatives of the characteristic function for the random variables of interest by two different methods; the comparison of the two different expressions for the time derivatives then yields the desired partial differential equations. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, STOCHASTIC PROCESSES), (*STOCHASTIC PROCESSES, PARTIAL DIFFERENTIAL EQUATIONS), EQUATIONS, STATISTICAL FUNCTIONS, STATISTICAL PROCESSES, PROBABILITY, NUMERICAL METHODS AND PROCEDURES

Distribution Statement : APPROVED FOR PUBLIC RELEASE