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In this article, we are concerned with a multidimensional degenerateparabolic-hyperbolic equation driven by Levy processes. Using bounded variation(BV) estimates for vanishing viscosity approximations, we derive an explicitcontinuous dependence estimate on the nonlinearities of the entropy solutionsunder the assumption that Levy noise depends only on the solution. This resultis used to show the error estimate for the stochastic vanishing viscositymethod. In addition, we establish fractional BV estimate for vanishingviscosity approximations in case the noise coefficients depend on both thesolution and spatial variable.

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