Weak solution for backward stochastic differential equations driven by fractional brownian motion

We introduce the concept of weak solution for Backward Stochastic Differential Equation driven by Fractional Brownian motion. By Girsanov theorem for fractional Brownian motion, we establish the equivalence of existence of weak solutions for two Backward Stochastic Differential Equation driven by Fractional Brownian Motion with different drift coefficients. We also give a sufficient condition to the existence of the weak solution.