Controlled ordinary differential equations with random path-dependent coefficients and stochastic path-dependent Hamilton-Jacobi equations
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DOI10.1016/J.SPA.2022.09.001zbMATH Open1500.49007arXiv2005.01232OpenAlexW3021448757WikidataQ115341098 ScholiaQ115341098MaRDI QIDQ2093689
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Publication date: 27 October 2022
Published in: (Search for Journal in Brave)
Abstract: This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns out to be a random field on the path spaces and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.
Full work available at URL: https://arxiv.org/abs/2005.01232
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