Quantitative compactness estimates for stochastic conservation laws
Kenneth H. Karlsen
TL;DR
This paper develops a quantitative compactness estimate for stochastic conservation laws, extending deterministic results to stochastic cases, and provides bounds on the convergence rate of solutions with vanishing viscosity.
Contribution
It introduces a stochastic version of Kruzkov's interpolation lemma, generalizing previous deterministic compactness estimates to stochastic conservation laws.
Findings
Provides a new bound on the rate of convergence for stochastic conservation laws.
Extends compensated compactness techniques to stochastic PDEs.
Offers a framework for analyzing the stability of solutions under stochastic perturbations.
Abstract
We present a quantitative compensated compactness estimate for stochastic conservation laws, which generalises a previous result of Golse & Perthame (2013) for deterministic equations. With a stochastic modification of Kruzkov's interpolation lemma, this estimate provides bounds on the rate at which a sequence of vanishing viscosity solutions becomes compact. This contribution is for the Proceedings of HYP2022.
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Taxonomy
TopicsStochastic processes and financial applications · Risk and Portfolio Optimization · Fluid Dynamics and Turbulent Flows