Optimal control for rough differential equations
نویسندگان
چکیده
In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index β > 1/2. We split our study in two cases. If the coefficient of dgt does not depend on the control process, we prove an existence theorem for a slightly generalized control problem, that is we obtain a literal extension of the corresponding deterministic situation. If the coefficient of dgt depends on the control process, we also prove an existence theorem but we are here obliged to restrict the set of controls to sufficiently regular functions.
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