This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than ). 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.
 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
 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
 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
 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
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