Averaging Principle for Backward Stochastic Differential Equations driven by both standard and fractional Brownian motions

Document Type : Regular research papers

Authors

1 Laboratoire de Mathématiques Appliquées (LMA), Département de Mathématiques et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, Fann, Dakar, Senega

2 LERSTAD, UFR Sciences Appliquées et de Technologie, Université Gaston Berger, Saint-Louis

3 UFR SATIC, Université Alioune Diop de Bambey, Bambey, Sénégal

Abstract

Stochastic averaging for a class of backward stochastic differential equations driven by both
standard and fractional Brownian motions (SFrBSDEs in short), is investigated.
An averaged SFrBSDEs for the original SFrBSDEs is proposed, and their solutions are quantitatively
compared. Under some appropriate assumptions, the solutions to original systems can be
approximated by the solutions to averaged stochastic systems in the sense of mean square

In this paper, we study the stochastic averaging principle for backward stochastic differential
equations driven by both standard and fractional Brownian motions (SFrBSDEs in short). An
averaged SFrBSDEs for the original SFrBSDEs is proposed, and their solutions are quantita-
tively compared. Under some appropriate assumptions, the solutions to original systems can
be approximated by the solutions to averaged stochastic systems in the sense of mean square.

Stochastic averaging for a class of backward stochastic differential equations driven by both
standard and fractional Brownian motions (SFrBSDEs in short), is investigated.
An aver-
aged SFrBSDEs for the original SFrBSDEs is proposed, and their solutions are quantitatively
compared.
Under some appropriate assumptions, the solutions to original systems can be
approximated by the solutions to averaged stochastic systems in the sense of mean square

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