Dynamic Programming of Stochastic Burgers Equation Driven by Levy Noise

2022/04/13 by Manil T. Mohan, Mohan, Manil T., K. Sakthivel +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.48550/arxiv.2204.06548

Abstract

In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Levy type noises with distributed control process acting on the state equation. We use the dynamic programming approach for the second order Hamilton-Jacobi- Bellman (HJB) equation consisting of an integro-differential operator with Levy measure associated with the stochastic control problem. Using the regularizing properties of the transition semigroup corresponding to the stochastic Burgers equation and compactness arguments, we solve the HJB equation and the resultant feedback control problem.

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• On the Navier-Stokes equations and the Hamilton-Jacobi-Bellman equation on the group of volume preserving diffeomorphisms

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