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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 16
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Original Articles

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

, &
Pages 2917-2927 | Received 10 Oct 2016, Accepted 22 Oct 2016, Published online: 04 Nov 2016
 

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.

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Notes

No potential conflict of interest was reported by the authors.

1 This proof is in fact coincides with that of [Citation14, 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.

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