Continuous dependence estimate for a degenerate parabolic-hyperbolic\n equation with Levy noise

2016/04/26 by Ujjwal Koley, Koley, Ujjwal, Ananta K. Majee +3
Economics, Econometrics and Finance · Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1604.07839

openalex publication_date 2016/04/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this article, we are concerned with a multidimensional degenerate\nparabolic-hyperbolic equation driven by Levy processes. Using bounded variation\n(BV) estimates for vanishing viscosity approximations, we derive an explicit\ncontinuous dependence estimate on the nonlinearities of the entropy solutions\nunder the assumption that Levy noise depends only on the solution. This result\nis used to show the error estimate for the stochastic vanishing viscosity\nmethod. In addition, we establish fractional BV estimate for vanishing\nviscosity approximations in case the noise coefficients depend on both the\nsolution and spatial variable.\n

Related

• Continuous dependence estimate for conservation laws with Lévy noise
• On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise
• A fractional degenerate parabolic-hyperbolic Cauchy problem with noise
• The Cauchy problem for a fractional conservation laws driven by Lévy noise
• Renormalized stochastic entropy solution for degenerate parabolic-hyperbolic equations with Levy noise