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arXiv · 2009.06866

Time fractional stochastic differential equations driven by pure jump Lévy noise

Peixue Wu·Zhiwei Yang·Hong Wang·Renming Song
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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 $L^p$ moment estimates on the solutions. As an application of moment estimates, we prove the Hölder regularity of the solutions.

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Peixue Wu, Zhiwei Yang, Hong Wang, Renming Song. 2024-12-22. Time fractional stochastic differential equations driven by pure jump Lévy noise. https://doi.org/10.1016/j.jmaa.2021.125412

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