单调连续条件下多值正倒向随机微分方程解的存在性

Existence of Solutions of Multivalued FBSDE with Continuous Monotone Coefficients

研究了一类线性增长单调连续系数的多值正倒向随机微分方程解的存在性,其中方程的终端时间T为任意有限常数、系数为随机的。应用连续线性增长函数可以用Lipschitz函数逼近、极大单调算子的Yosida估计和随机微分方程的比较定理,得到了方程存在一个适应解。

The existence of solutions of Forward-Backward Stochastic Differential Equations（FBSDE for short） under linear growth and continuous monotone coefficients is studied,the terminal time T is finite constant and the coefficients are random.By means of approximation of linear continuous function by Lipschitz functions,Yosida approximation of maximal monotone operator and comparison results of Stochastic Differential Equations,the existence of solutions of FBSDE is obtained.