Sufficient Conditions for a First Passage Time Process to be that of Brownian Motion

1 April 1969

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 6 (1) , 218-223
https://doi.org/10.2307/3212290

Abstract

In this paper we assign a set of conditions to a strong Markov process and arrive at a differential equation analogous to the Kolmogorov equation. However, in this case the duration variable is the net distance travelled and the state variable is a time, a situation precisely opposite to that of Brownian motion. Solving this differential equation under certain boundary conditions produces the density function of the first passage times of Brownian motion with positive drift (see [1]), with the aid of which we define a new stochastic process.

Keywords

SUFFICIENT CONDITIONS
PASSAGE TIME
BROWNIAN MOTION
TIME PROCESS

This publication has 1 reference indexed in Scilit:

Statistical Properties of Inverse Gaussian Distributions. I
The Annals of Mathematical Statistics, 1957