The Cauchy problem for fractional conservation laws driven by Lévy noise

Neeraj Bhauryal, Ujjwal Koley and Guy Vallet

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5310-5365

Abstract: In this article, we explore some of the main mathematical problems connected to multidimensional fractional conservation laws driven by Lévy processes. Making use of an adapted entropy formulation, a result of existence and uniqueness of a solution is established. Moreover, using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that the Lévy noise depends only on the solution. This result is used to show the error estimate for the stochastic vanishing viscosity method. Furthermore, we establish a result on vanishing non-local regularization of scalar stochastic conservation laws.

Keywords: Fractional conservation laws; Lévy noise; Young measures; Wellposedness; Stability (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.03.009

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