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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2021 Number 7, Pages 30–42 (Mi ivm9693)

Iterative method for non-adapted fuzzy stochastic differential equations

H. Jafari

Department of Mathematics, Chabahar Maritime University, Chabahar, Iran

Abstract: In this paper, an anticipating stochastic differential equation is considered, that the integrand processes are not adapted to the filtration generated by a Wiener process. Using the correspondence between the Skorohod integral and Itô-Skorohod integral, the equations can be solved by using standard iterative techniques. Then, the existence and uniqueness of strong solutions to these equations are discussed. Such equations with non-adapted, fuzziness, and randomness processes can be applied in financial models.

Keywords: Malliavin calculus, fuzzy stochastic process, fuzzy stochastic integral, Skorohod integral.

UDC: 517

Received: 20.07.2020
Revised: 11.03.2021
Accepted: 30.03.2021

DOI: 10.26907/0021-3446-2021-7-30-42


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, 65:7, 24–34


© Steklov Math. Inst. of RAS, 2024