Martingale solution to stochastic Korteweg - de Vries equation driven by L\'evy noise
Anna Karczewska, Maciej Szczeci\'nski
TL;DR
This paper establishes the existence of martingale solutions for the stochastic Korteweg-de Vries equation influenced by Lévy noise, combining Galerkin methods and auxiliary results for the proof.
Contribution
It introduces a novel existence proof for solutions to the stochastic Korteweg-de Vries equation driven by Lévy noise using Galerkin approximation.
Findings
Existence of martingale solutions proven.
Application of Galerkin approximation method.
Use of auxiliary results tailored for Lévy noise.
Abstract
We study stochastic Korteweg - de Vries equation driven by L\'evy noise consisting of the compensated time homogeneous Poisson random measure and a cylindrical Wiener process. We prove the existence of a martingale solution to the equation studied. In proof of the existence theorem we use the Galerkin approximation and several auxiliary results suitable for the problem considered.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stochastic processes and financial applications · Stability and Controllability of Differential Equations