# Accession Number:

## AD0604947

# Title:

## A SYSTEMATIC APPROACH TO A CLASS OF PROBLEMS IN THE THEORY OF NOISE AND OTHER RANDOM PHENOMENA,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1955-09-10

# Pagination or Media Count:

## 22.0

# Abstract:

The problem of finding the probability distribution of a functional, consisting of a multi-dimensional Markoff process and a given function, appears in many forms in the theory of noise and other random phenomena. It is shown that a certain function from which this probability distri bution can be obtained is the unique solution of two integral equations. A perturbation formalism which relates the solutions of the integral equations belonging to two different functions is developed. If the transition probability density is the principal solution of two partial differential equations of the Fokker-Planck-Kolmogoroff type, the principal solution of two similar differential equations is the solution of the integral equations. As an example the probability distribution of the sample probability density for a stationary Markoff process is calculated. Author