The Cauchy problem for fractional conservation laws driven by Lévy noise
| Autor: | Neeraj Bhauryal, Guy Vallet, Ujjwal Koley |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Conservation law Mathematical problem Applied Mathematics 010102 general mathematics 01 natural sciences Lévy process 010101 applied mathematics [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Levy noise Modeling and Simulation Bounded variation Initial value problem Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Uniqueness 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Stochastic Processes and their Applications Stochastic Processes and their Applications, Elsevier, 2020, 130 (9), pp.5310-5365. ⟨10.1016/j.spa.2020.03.009⟩ |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2020.03.009⟩ |
| Popis: | In this article, we explore some of the main mathematical problems connected to multidimensional fractional conservation laws driven by Levy 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 Levy 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. |
| Databáze: | OpenAIRE |
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