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The Cauchy problem for fractional conservation laws driven by Lévy noise

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  • Bhauryal, Neeraj
  • Koley, Ujjwal
  • Vallet, Guy

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.

Suggested Citation

  • Bhauryal, Neeraj & Koley, Ujjwal & Vallet, Guy, 2020. "The Cauchy problem for fractional conservation laws driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5310-5365.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5310-5365
    DOI: 10.1016/j.spa.2020.03.009
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    References listed on IDEAS

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    1. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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