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# Accession Number:

## AD0603986

# Title:

## THE FIRST PASSAGE PROBLEM FOR A CONTINUOUS MARKOFF PROCESS

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CA

# 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#