Convergent finite difference schemes for stochastic transport equations

Abstract

We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required for deterministic transport equations. The $L^2$ estimate, crucial for the analysis, is obtained through a discrete duality argument and a comprehensive examination of a class of backward parabolic difference schemes.

42 pages; minor amendments and typos corrected

References in corpus (6)

• Well-posedness of the transport equation by stochastic perturbation
• Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness
• Probabilistic analysis of the upwind scheme for transport
• Convergence rates for upwind schemes with rough coefficients
• On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions
• Analysis of the implicit upwind finite volume scheme with rough coefficients