# Accession Number:

## AD0425087

# Title:

## LIKELIHOOD RATIOS FOR STOCHASTIC PROCESSES RELATED BY GROUPS OF TRANSFORMATION,

# Descriptive Note:

# Corporate Author:

## MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

# Personal Author(s):

# Report Date:

## 1962-01-26

# Pagination or Media Count:

## 19.0

# Abstract:

If xt and yt are stochastic processes with the same parameter set, they induce measures m sub x and m sub y on a suitably chosen space of sample functions. It is an impotant problem of statistics to find conditions guaranteeing the existence of the Radon-Nikodym derivative or likelihood ratio dm sub xdm sub y and to find formulas for computing it. These derivatives are also helpful in describing one process in terms of the other, in particular, in carrying almost everywhere properties from one process to another which is less well known. A technique is developed which relies less on such computations and more on assumed geometrical relationships between the processes. This technique has already been applied to the mean value problem, yt xt ft for a fixed ft when xt is the solution of a diffusion equation. Author