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A class of laplace transforms arising in a diffusion problem
Author(s) -
Berman S. M.
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160470106
Subject(s) - laplace transform , mathematics , real line , constant (computer programming) , class (philosophy) , brownian motion , diffusion , mathematical analysis , property (philosophy) , distribution (mathematics) , function (biology) , diffusion process , pure mathematics , physics , statistics , computer science , philosophy , knowledge management , innovation diffusion , epistemology , artificial intelligence , evolutionary biology , biology , thermodynamics , programming language
It is shown that the function [α + (1 + 2 s ) 1/2 ] −1 , s ≥ 0, with fixed α ≥ −1, is the Laplace transform of an explicitly given non‐negative function g(x ;α), × ≥ 0. This class of functions has easily computable convolutions. This property is used to identify the distribution of a sojourn time integral for the diffusion defined as Brownian motion on the real line with constant drift to the origin. © 1994 John Wiley & Sons, Inc.