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Deplay BSDEs driven by fractional Brownian motion

Sadibou Aidara and Ibrahima Sane


This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.

Communicated by Stanislav Molchanov


[1] S. Aidara and Y. Sagna, BSDEs driven by two mutually independent fractional Brownian motions with stochastic Lipschitz coefficients, Appl. Math. Nonlinear Sci. 4 (2019), no. 1, 151–162. 10.2478/AMNS.2019.1.00014Search in Google Scholar

[2] S. Aidara and A. B. Sow, Generalized fractional BSDE with non Lipschitz coefficients, Afr. Mat. 27 (2016), no. 3–4, 443–455. 10.1007/s13370-015-0354-3Search in Google Scholar

[3] C. Bender, Explicit solutions of a class of linear fractional BSDEs, Systems Control Lett. 54 (2005), no. 7, 671–680. 10.1016/j.sysconle.2004.11.006Search in Google Scholar

[4] Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions, Mem. Amer. Math. Soc. 175 (2005), 1–127. 10.1090/memo/0825Search in Google Scholar

[5] Y. Hu and S. Peng, Backward stochastic differential equation driven by fractional Brownian motion, SIAM J. Control Optim. 48 (2009), no. 3, 1675–1700. 10.1137/070709451Search in Google Scholar

[6] X. Mao, Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Process. Appl. 58 (1995), no. 2, 281–292. 10.1016/0304-4149(95)00024-2Search in Google Scholar

[7] L. Maticiuc and T. Nie, Fractional backward stochastic differential equations and fractional backward variational inequalities, J. Theoret. Probab. 28 (2015), no. 1, 337–395. 10.1007/s10959-013-0509-9Search in Google Scholar

[8] E. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), no. 1, 55–61. 10.1016/0167-6911(90)90082-6Search in Google Scholar

[9] Y. Wang and Z. Huang, Backward stochastic differential equations with non-Lipschitz coefficients, Statist. Probab. Lett. 79 (2009), no. 12, 1438–1443. 10.1016/j.spl.2009.03.003Search in Google Scholar

Received: 2020-12-10
Accepted: 2021-08-15
Published Online: 2022-01-06
Published in Print: 2022-03-01

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