The Equivalence between Uniqueness and Continuous Dependence of Solution for BSDEs with Continuous Coefficient
نویسندگان
چکیده
where the terminal condition ξ and the coefficient g = g(t, y, z) are given. W is a d–dimensional Brownian motion. The solution (yt, zt)t∈[0,T ] is a pair of square integrable processes. A foundational and interesting problem is: what is the relationship between the uniqueness of solution and continuous dependence with respect to g or ξ? In the standard situation where g satisfies linear growth condition and Lipschitz condition in (y, z), it has been proved by Pardoux and Peng [4] that there exists a unique solution. In this case, the continuous dependence with respect to g and ξ is is described by the following inequality (see El Karoui, Peng and Quenez [1]):
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