论文标题
对于半线性抛物线SPDE的解决方案的Malliavin可不同性
On pointwise Malliavin differentiability of solutions to semilinear parabolic SPDEs
论文作者
论文摘要
我们在固定点和空间上评估了对$ \ Mathbb {r}^d $的有界域上的一类抛物面耗散随机PDES的轻度溶液的一阶Malliavin衍生物的估计。特别是，此类方程是由乘法维也纳噪声驱动的，非线性漂移项是与局部Lipschitz连续函数相关的叠加算子，可满足合适的多项式生长界限。主要论点依赖于良好的理论，从温和的意义上讲，在Banach空间，单调性和比较原理中的随机演化方程。
We obtain estimates on the first-order Malliavin derivative of mild solutions, evaluated at fixed points in time and space, to a class of parabolic dissipative stochastic PDEs on bounded domain of $\mathbb{R}^d$. In particular, such equations are driven by multiplicative Wiener noise and the nonlinear drift term is the superposition operator associated to a locally Lipschitz continuous function satisfying suitable polynomial growth bounds. The main arguments rely on the well-posedness theory in the mild sense for stochastic evolution equations in Banach spaces, monotonicity, and a comparison principle.
