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, Pages 1-12 PDF (545.56 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2023.205663.1025 | ||
| Authors | ||
| Sadibou AIDARA* 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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