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Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations.
- Source :
-
Mathematics & Computers in Simulation . Mar2022, Vol. 193, p269-279. 11p. - Publication Year :
- 2022
-
Abstract
- This paper is devoted to the rigorous derivation of some discrete versions of stochastic Grönwall inequalities involving a martingale, which are commonly used in the numerical analysis of multi-term stochastic time-fractional diffusion equations. A Grönwall lemma is also established to deal with the numerical analysis of multi-term stochastic fractional diffusion equations with delay. The proofs of the established inequalities are based on a corresponding deterministic version of the discrete fractional Grönwall lemma in case of smooth solutions and an inequality bounding the supremum in terms of the infimum for discrete time martingales. A numerical application is introduced finally in which the constructed inequalities are handled to derive a priori estimates for a discrete fractional stochastic model. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03784754
- Volume :
- 193
- Database :
- Academic Search Index
- Journal :
- Mathematics & Computers in Simulation
- Publication Type :
- Periodical
- Accession number :
- 153900829
- Full Text :
- https://doi.org/10.1016/j.matcom.2021.10.013