Accession Number : ADA185592

Title :   Diffusion First Passage Times: Approximations and Related Differential Equations,

Corporate Author : FORD AEROSPACE AND COMMUNICATIONS CORP PALO ALTO CA

Personal Author(s) : Wenocur, Michael L

PDF Url : ADA185592

Report Date : Jan 1986

Pagination or Media Count : 27

Abstract : This paper is primarily concerned with computing first passage time statistics. In previous work a general reliability model was proposed in which system failures occur when either system wear-and-tear reaches some maximum permissible level (ie, a first passage occurs), or when some killing event happens (such killing events occur with rate k(x) in state x). Under this model w(x,t) satisfies a certain equation: It is possible to solve for w(x,t) and related quantities with methods very similar to those presented here. In Section 2, algorithms for approximating w(x,t) are obtained. In particular, the infinite spectral expansion for w(x,t) is approximated by an n-term sub-expansion which matches the first n-1 moments. Section 2 concludes with some remarks about out preliminary computational experience. In Sections 3 and 4, methods are given for obtaining the eigenvalues and first passage moments, necessary for computing approximations to w(x,t). In Section 5, computational issues related to calculating the moment generating function are considered. Section 6 and 7 include theoretical complements about first passage times. In particular, the moment generating function is shown to possess an interesting representation having exponential form. This exponential representation is related to asymptotic expansions used in analyzing perturbations of certain second-order differential equations.

Descriptors :   *STATISTICAL DISTRIBUTIONS, *TIME STUDIES, ALGORITHMS, ASYMPTOTIC SERIES, DIFFERENTIAL EQUATIONS, EIGENVALUES, EXPANSION, MOMENTS, RELIABILITY, SPECTRA, STATISTICS, TIME, MATHEMATICAL MODELS, APPROXIMATION(MATHEMATICS), BROWNIAN MOTION, COMPUTATIONS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE