On existence of optimal solutions for stochastic differential inclusions with mean derivatives

Abstract

For a stochastic differential inclusion given in terms of mean derivatives, we prove the existence of optimal solution minimizing a certain cost criterion.

Keywords:

• mean derivatives
• stochastic differential inclusions
• optimal solution

AMS Subject Classifications:

• 58J65
• 60H10

Acknowledgments

The research is supported in part by RFBR Grants 10-01-00143 and 12-01-00183.