Stochastic Control of Tidal Dynamics Equation with Levy Noise

TL;DR

This paper studies the mathematical properties of a tidal dynamics model influenced by Levy noise, proving existence and uniqueness of solutions and establishing optimal control strategies using advanced stochastic analysis techniques.

Contribution

It introduces a rigorous analysis of the tidal dynamics equation with Levy noise, including existence, uniqueness, regularity, and optimal control formulation.

Findings

Proved existence and uniqueness of strong solutions.

Established regularity of solutions.

Demonstrated existence of optimal controls.

Abstract

In this work we first present the existence, uniqueness and regularity of the strong solution of the tidal dynamics model perturbed by L\'evy noise. Monotonicity arguments have been exploited in the proofs. We then formulate a martingale problem of Stroock and Varadhan associated to an initial value control problem and establish existence of optimal controls.