Accession Number : AD0672207

Title :   RANDOM ORDINARY DIFFERENTIAL EQUATIONS.

Descriptive Note : Technical rept. Sep 67-Jun 68,

Corporate Author : CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS

Personal Author(s) : Edsinger,R.

Report Date : JUN 1968

Pagination or Media Count : 52

Abstract : Existence and uniqueness theorems are proved for solutions (in the mean) of the random differential equation x' = f(t,x,omega). This is accomplished by determining when a sample path solution is also a solution in the mean. The usual definition of mean stability is generalized to a more useful form. Theorems are developed which relate this general type stability to the stability of the 'average problem'. Finally theorems relating almost sure stability with the stability of the average problem are proved. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, PROBLEM SOLVING), (*FUNCTIONAL ANALYSIS, DIFFERENTIAL EQUATIONS), NONLINEAR DIFFERENTIAL EQUATIONS, MEASURE THEORY, MATRICES(MATHEMATICS), STATISTICAL PROCESSES, BANACH SPACE, STABILITY, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE