Averaging Principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients
AIDARA, S., Ndiaye, B., Sow, A. (2024). Averaging Principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients. EKB Journal Management System, 12(1), 1-12. doi: 10.21608/ejmaa.2023.205663.1025
Sadibou AIDARA; Bidji Ndiaye; Ahmadou Bamba Sow. "Averaging Principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients". EKB Journal Management System, 12, 1, 2024, 1-12. doi: 10.21608/ejmaa.2023.205663.1025
AIDARA, S., Ndiaye, B., Sow, A. (2024). 'Averaging Principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients', EKB Journal Management System, 12(1), pp. 1-12. doi: 10.21608/ejmaa.2023.205663.1025
AIDARA, S., Ndiaye, B., Sow, A. Averaging Principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients. EKB Journal Management System, 2024; 12(1): 1-12. doi: 10.21608/ejmaa.2023.205663.1025

Averaging Principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients

Electronic Journal of Mathematical Analysis and Applications
Volume 12, Issue 1, January 2024, Page 1-12  XML PDF (545.56 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2023.205663.1025
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Authors
Sadibou AIDARA email 1; Bidji Ndiaye2; Ahmadou Bamba Sow2
1Université Gaston Berger
2UGB
Abstract
Stochastic averaging for a class of backward stochastic differential equations with fractional Brownian motion, of the Hurst parameter $ H $ in the interval $ \left( \frac{1}{2}, 1 \right) $, is investigated under the non Lipschitz condition. An averaged backward stochastic differential equations with fractional Brownian motions for the original backward stochastic differential equations with fractional Brownian motion 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, both in the sense of mean square and also in probability. The stochastic integral used throughout the paper is the divergence type integral.










Stochastic averaging for a class of backward stochastic differential equations with fractional Brownian motion, of the Hurst parameter $ H $ in the interval $ \left( \frac{1}{2}, 1 \right) $, is investigated under the non Lipschitz condition. An averaged backward stochastic differential equations with fractional Brownian motions for the original backward stochastic differential equations with fractional Brownian motion 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, both in the sense of mean square and also in probability. The stochastic integral used throughout the paper is the divergence type integral.
Keywords
Averaging principle; backward stochastic differential equation; fractional Brownian motion
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