The Implicit Euler Scheme for FSDEs with Stochastic Forcing: Existence and Uniqueness of the Solution

Kęstutis Kubilius ()
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Kęstutis Kubilius: Faculty of Mathematics and Informatics, Vilnius University, Akademijos g. 4, LT-08412 Vilnius, Lithuania

Mathematics, 2024, vol. 12, issue 16, 1-18

Abstract: In this paper, we focus on fractional stochastic differential equations (FSDEs) with a stochastic forcing term, i.e., to FSDE, we add a stochastic forcing term. Using the implicit scheme of Euler’s approximation, the conditions for the existence and uniqueness of the solution of FSDEs with a stochastic forcing term are established. Such equations can be applied to considering FSDEs with a permeable wall.

Keywords: stochastic differential equations; stochastic forcing; fractional Brownian motion; implicit Euler scheme; p-variation; Pearson model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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