| Keywords and phrases: fractional Brownian motion backward stochastic differential equations, Malliavin derivative and fractional Itô’s formula
Received: June 25, 2024; Revised: August 25, 2024; Accepted: September 14, 2024; Published: October 25, 2024
How to cite this article: Yaya SAGNA, Lamine SYLLA and Sadibou AIDARA, Generalized backward stochastic differential equations driven by two mutually independent fractional Brownian motions, Advances in Differential Equations and Control Processes 31(4) (2024), 627-650. https://doi.org/10.17654/0974324324032
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License  
References:
[1] S. Aidara and Y. Sagna, BSDEs driven by two mutually independent fractional Brownian motions with stochastic Lipschitz coefficients, Applied Mathematics and Nonlinear Sciences 4(1) (2019), 151162.
[2] S. Aidara and L. Sylla, BSDEs driven by fractional Brownian motion with time-delayed generators, Applicable Analysis 4(103) (2023), 724-733.
[3] Y. Guo, M. Chen, X. B. Shu, et al., The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm, Stochastic Analysis and Applications 4(39) (2021), 643-666.
[4] K. J. Borkowska, Generalized BSDEs driven by fractional Brownian motion, Stat. Prob. Lett. (83) (2013), 805-811.
[5] L. Decreusefond and A. S. Ustunel, Stochastic analysis of the fractional Brownian motion, Potential Anal. (10) (1998), 177-214.
[6] W. Fei, D. Xia and S. Zhang, Solutions to BSDEs driven by both standard and fractional Brownian motions, Acta Mathematicae Applicatae Sinica, English Series (29) (2013), 329-354.
[7] Y. Hu, Integral transformation and anticipative calculus for fractional Brownian motion, Mem. Amer. Math. Soc. (175) (2005).
[8] Y. Hu and S. Peng, Backward stochastic differential equation driven by fractional Brownian motion, SIAM J. Control Optim. (48) (2009), 1675-1700.
[9] L. Li, J. G. Liu and J. Lu, Fractional stochastic differential equations satisfying fluctuation-dissipation theorem, Journal of Statistical Physics (169) (2017), 316 339.
[10] L. Maticiuc and T. Nie, Fractional Backward stochastic differential equations and fractional backward variational inequalities, 2012. Arxiv : 1102.3014v3 [mathPR].
[11] I. Norros, On the use of fractional Brownian motion in the theory of connectionless networks, Preprint, 1994.
[12] I. Norros, A storage model with self-similar input, Queueing Systems Theory Appl. 3-4(16) (1994), 387-396.
[13] I. Norros, Four approaches to the fractional Brownian storage, Queueing Systems Theory Appl., Preprint, 1994.
[14] E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. (14) (1990), 55-61.
[15] Y. Wang and Z. Huang, Backward stochastic differential equations with non-Lipschitz coefficients, Statistics and Probability Letters (79) (2009), 1438-1443.
[16] L. C. Young, An inequality of the Hölder type connected with Stieltjes integration, Acta Math. (67) (1936), 251-282.
|
