2006/06/01 by Laurent Mazliak, Mazliak, Laurent, Ivan Nourdin +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stability and Controllability of Differential Equations #math.OC #math.PR
paper · pdf · doi:10.48550/arxiv.math/0606030
13 pages
arxiv created 2006/06/01 · openalex publication_date 2006/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg_t 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 dg_t 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.