Time fractional stochastic differential equations driven by pure jump Lévy noise

Peixue Wu, Zhiwei Yang, Hong Wang, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we introduce a variable order time fractional differential equation driven by pure jump Lévy noise, which models the motion of a particle exhibiting memory effect. We prove the well-posedness of this equation without assuming any integrability condition on the initial condition and the large jump coefficient, by using a truncation argument. Under some extra conditions, we also derive some Lp moment estimates on the solutions. As an application of moment estimates, we prove the Hölder regularity of the solutions.

Original languageEnglish (US)
Article number125412
JournalJournal of Mathematical Analysis and Applications
Volume504
Issue number2
DOIs
StatePublished - Dec 15 2021

Keywords

  • Moment estimates
  • Regularity
  • Time fractional stochastic differential equation
  • Variable-order
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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