Accession Number:

AD0603986

Title:

THE FIRST PASSAGE PROBLEM FOR A CONTINUOUS MARKOFF PROCESS

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CA

Personal Author(s):

Report Date:

1953-03-02

Pagination or Media Count:

33.0

Abstract:

The solution to the first passage problem for a strongly continuous temporally homogeneous Markoff process Xt is given. If T T sub ab x is a random variable giving the time of first passage of X t from the region a Xt b when a X0 x b, simple methods of getting the distribution of T at least in terms of a Laplace transform are developed. From the distribution of T the distribution of the maximum of Xt and the range of Xt are deduced. These results yield, in an asymptotic form, solutions to certain statistical problems in sequential analysis, non-parametric theory of goodness of fit, optional stopping, etc. which are treated as an illustration of the theory.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE