在生成元g的第i个分量gi(t,y,z)仅仅依赖于矩阵z的第i行的条件下,Hamadene于2003年证明了生成元一致连续的倒向随机微分方程的L2解的存在性,其L2解的唯—性由范胜君等于2010年得到.本文进一步地证明了该类倒向随机微分方程的L^p(P〉1)解的存在唯一性.
In 2003, Hamadene proved the existence of L2 solutions to multidimensional backward stochastic differential equations (or BSDEs for short) with uniformly continuous generators, provided that the ith component gi(t, y, z) of the generator g depends only on the ith row of the matrix z. The uniqueness of L2 solutions was obtained by Fan et al. in 2010. In this paper, the authors further prove the existence and uniqueness of Lp (p 〉1) solutions to this kind of BSDEs.