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Near-Relaxed Control Problem of Fully Coupled Forward–Backward Doubly System

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Abstract

In this paper, we are concerned with an optimal control problem where the system is driven by a fully coupled forward–backward doubly stochastic differential equation. We study the relaxed model for which an optimal solution exists. This is an extension of initial control problem, where admissible controls are measure valued processes. We establish necessary as well as sufficient optimality conditions to the relaxed one.

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Acknowledgments

This work was partially supported by the Algerian PNR project N: 8/u07/857.

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  1. Laboratory of Applied Mathematics, University Mouhamed Kheider, P.O. Box 145, 07000, Biskra, Algeria

    Adel Chala

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  1. Adel Chala
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Correspondence to Adel Chala.

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Chala, A. Near-Relaxed Control Problem of Fully Coupled Forward–Backward Doubly System. Commun. Math. Stat. 3, 459–476 (2015). https://doi.org/10.1007/s40304-015-0068-8

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  • DOI: https://doi.org/10.1007/s40304-015-0068-8

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