Time fractional stochastic differential equations driven by pure jump Lévy noise

Peixue Wu; Zhiwei Yang; Hong Wang; Renming Song

doi:10.1016/j.jmaa.2021.125412

Time fractional stochastic differential equations driven by pure jump Lévy noise

Peixue Wu, Zhiwei Yang, Hong Wang, Renming Song

Research output: Contribution to journal › Article › peer-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 L^p moment estimates on the solutions. As an application of moment estimates, we prove the Hölder regularity of the solutions.

Original language	English (US)
Article number	125412
Journal	Journal of Mathematical Analysis and Applications
Volume	504
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2021.125412
State	Published - Dec 15 2021

Keywords

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

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2021.125412

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title = "Time fractional stochastic differential equations driven by pure jump L{\'e}vy noise",

abstract = "In this paper we introduce a variable order time fractional differential equation driven by pure jump L{\'e}vy 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 H{\"o}lder regularity of the solutions.",

keywords = "Moment estimates, Regularity, Time fractional stochastic differential equation, Variable-order, Well-posedness",

author = "Peixue Wu and Zhiwei Yang and Hong Wang and Renming Song",

note = "Funding Information: We thank the referees for the constructive and helpful comments, which greatly improved the quality of this paper. This work was funded in part by the Army Research Office (ARO) MURI Grant W911NF-15-1-0562 , by the National Science Foundation under Grants DMS-1620194 and DMS-2012291 , and by the Simons Foundation (# 429343 ). Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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doi = "10.1016/j.jmaa.2021.125412",

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T1 - Time fractional stochastic differential equations driven by pure jump Lévy noise

AU - Wu, Peixue

AU - Yang, Zhiwei

AU - Wang, Hong

AU - Song, Renming

N1 - Funding Information: We thank the referees for the constructive and helpful comments, which greatly improved the quality of this paper. This work was funded in part by the Army Research Office (ARO) MURI Grant W911NF-15-1-0562 , by the National Science Foundation under Grants DMS-1620194 and DMS-2012291 , and by the Simons Foundation (# 429343 ). Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/12/15

Y1 - 2021/12/15

N2 - 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.

AB - 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.

KW - Moment estimates

KW - Regularity

KW - Time fractional stochastic differential equation

KW - Variable-order

KW - Well-posedness

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Time fractional stochastic differential equations driven by pure jump Lévy noise

Abstract

Keywords

ASJC Scopus subject areas

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