Accession Number : AD0609826

Title :   ON THE RELATION BETWEEN ORDINARY AND STOCHASTIC DIFFERENTIAL EQUATIONS,

Corporate Author : CALIFORNIA UNIV BERKELEY ELECTRONICS RESEARCH LAB

Personal Author(s) : Wong,Eugene ; Zakai,Moshe

Report Date : 11 AUG 1964

Pagination or Media Count : 37

Abstract : The following problem is considered in this paper: het x sub t be a solution to the stochastic differential equation: dx sub t = m(x sub t, t)dt + S(x sub t, t) dy sub t where y sub t is the Brownian motion process. het the nth derivative of x sub t be the solution to the ordinary differential equation which is obtained from the stochastic differential equation by replacing y sub t with the nth derivative of y sub t where this derivative is a continuous piecewise linear approximation to the Brownian motion and converges to y sub t as n approaches infinity. If x sub t is the solution to the stochastic differential equation (in the sense of Ito) does the sequence of the solutions converge to x sub t. It is shown that the answer is in general negative; it is, however, shown that the nth derivative of x sub t converges in the mean to the solution of another stochastic differential equation which is given.

Descriptors :   (*DIFFERENTIAL EQUATIONS, STOCHASTIC PROCESSES), (*STOCHASTIC PROCESSES, DIFFERENTIAL EQUATIONS), INTEGRALS, PROBABILITY, EQUATIONS, INEQUALITIES, SEQUENCES(MATHEMATICS), SERIES(MATHEMATICS), STATISTICAL FUNCTIONS, THEOREMS, VECTOR ANALYSIS, ANALYSIS OF VARIANCE, MOTION

Distribution Statement : APPROVED FOR PUBLIC RELEASE