论文标题
反射的预期向后随机微分方程具有非线性电阻
Reflected anticipated backward stochastic differential equations with nonlinear resistance
论文作者
论文摘要
在本文中，我们考虑了反射的预期的向后随机微分方程（简称Rabsdes），并在发电机中具有额外的电阻。首先，我们研究了存在和独特性结果。在Luo（2020）中，需要很小的时间范围的状况。与LUO（2020）中的证明方法相比，我们使用另一种证据的方法来避免需要发电机的Lipschitz系数$ f（t，y，z，θ，\ vartheta，m，m，\ bar {m}）$ for $ y，z，z，z，θ，\ vartheta $要小。我们只需要Lipschitz系数即可在发电机中的电阻足够小。此外，指定了解决方案的概率结构。其次，我们为这种类型的方程提供了比较定理。最后，在线性生长条件和电阻方面的其他一些条件下，我们得出了最小的溶液。
In this paper, we consider reflected anticipated backward stochastic differential equations (RABSDEs, for short) with an additional resistance in the generators. Firstly, we study the existence and uniqueness results. In Luo (2020), the condition of a small time horizon is needed. Compared with the proving method in Luo (2020), we use a different proving method to avoid requiring the Lipschitz coefficients of generators $f(t,y,z,θ,\vartheta,m,\bar{m})$ for $y,z,θ,\vartheta$ to be small enough. We only require the Lipschitz coefficient for resistance in generator is small enough. Moreover, a probabilistic structure for solution is specified. Secondly, we give a comparison theorem for this type of equation. At last, under the linear growth condition and some other conditions on resistance , we derive the minimal solution.
