On existence of optimal solutions for stochastic differential equations and inclusions with current velocities

Abstract

For a stochastic differential inclusion given in terms of current velocities (symmetric mean derivatives) on flat n-dimensional torus, we prove the existence of optimal solution minimizing a certain cost criterion. Then this result is applied to the problem of optimal control for equations with current velocities.

Keywords:

• Mean derivatives
• current velocities
• stochastic differential inclusions
• optimal solution

AMS Subject Classifications:

• 58J65
• 60H10

Notes

No potential conflict of interest was reported by the authors.

1 This proof is in fact coincides with that of [14, Theorem 2] but we include it here for completeness

Additional information

Funding

The research is supported in part by RSF [grant number 14-21-00066] carried out at Voronezh State University.