On the maximal and minimal solutions of  a nonlocal problem of  a delay stochastic differential equation

A. M. A. El-Sayeda,∗, F. Gaafarb and M. El-Gendyc

On the maximal and minimal solutions of a nonlocal problem of a delay stochastic differential equation

Authors :

A. M. A. El-Sayed^a,∗, F. Gaafar^b and M. El-Gendy^c

Author Address :

^a,b,cDepartment of Mathematics, College of science, Alexandria university, Egypt.

*Corresponding author.

Abstract :

In this paper we are concerned with a problem of of a delay stochastic differential equation with nonlocal condition, the solution is represented as stochastic integral equation that contain mean square Riemann integral. We study the existence of at least mean square continuous solution for this problem. The existence of the maximal and minimal solutions will be proved.

Keywords :

Nonlocal condition, delay equation, random Caratheodory function, stochastic Lebesgue dominated convergence theorem, at least mean square continuous solution, maximal solution, minimal solution.

DOI :

Article Info :

Received : May 10, 2016; Accepted : July 07, 2016.