不连续系数重倒向随机微分方程(BDSDE)解的存在性

The Existence of Backward Doubly Stochastic Differential Equations(BDSDE)with Discontinuous Coefficient

在不连续条件下对重倒向随机微分方程(BDSDE)y_t=ξ+∫Ttf(s,y_s,z_s)d_s+∫Ttg(s,y_s,z_s)dB_s-∫Ttz_sdW_s解的存在性进行了研究。在仅仅方程的系数满足线性增长和连续性条件下建立了新的比较定理,构造了一个单调有界的解序列,从而在弱的假设下建立此对类方程了解的存在性定理。该研究结果一般化和改进了一些已有结果。

In this paper,a class of backward doubly stochastic differential equations with discontinuous(left continuous)coefficients are studied.By establishing a new comparison theorem under linear growth and continuous condition,a monotone and bounded solution sequence is established,then an existence theorem of the solution to these equations is established under some weaker assumpation.The results generalize and improve some known results.