Averaging principle for BSDEs driven by two mutually independent fractional Brownian motions

This work considers stochastic partial differential equations (SPDEs) driven by fractional Brownian motions (fBm) with random delays modulated by two-time scale Markov switching processes leading to a two-time scale formulation. The two-time scale Markov chains have a fast-varying component and a slowly evolving component. Our aim is to obtain an averaging principle for such systems. Under suitable conditions, it is proved that there is a limit process in which the fast changing “noise” is averaged out. The slow component has a limit that is an average with respect to the stationary distribution of the fast component. The limit process is substantially simpler than the original system leading to reduction of the computational complexity.

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Anticipated BSDEs driven by two mutually independent fractional Brownian motions with non-Lipschitz coefficients

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2051 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Sadibou Aidara ◽

Yaya Sagna

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Existence And Uniqueness ◽

Stochastic Integral ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Type Integral ◽

Divergence Type ◽

Mutually Independent ◽

Uniqueness Of A Solution

Abstract This paper deals with a class of anticipated backward stochastic differential equations driven by two mutually independent fractional Brownian motions. We essentially establish the existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.

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BSDEs driven by two mutually independent fractional Brownian motions with stochastic Lipschitz coefficients

Applied Mathematics and Nonlinear Sciences ◽

10.2478/amns.2019.1.00014 ◽

2019 ◽

Vol 4 (1) ◽

pp. 139-150 ◽

Cited By ~ 6

Author(s):

Sadibou Aidara ◽

Yaya Sagna

Keyword(s):

Differential Equation ◽

Existence And Uniqueness ◽

Stochastic Integral ◽

Backward Stochastic Differential Equation ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Type Integral ◽

Divergence Type ◽

Mutually Independent ◽

Uniqueness Of A Solution

AbstractThis paper deals with a class of backward stochastic differential equation driven by two mutually independent fractional Brownian motions. We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.

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