希尔伯特空间中半线性随机发展方程的Trotter-Kato逼近
Trotter-Kato approximations of semilinear stochastic evolution equations in Hilbert spaces
摘要：
受T. E. Govindan在[5，8，9]中的结果，本文研究了一个更一般的半线性随机发展方程。本文所考虑的方程与前一个方程的不同之处在于，它对随机积分中的非线性函数做了一些改变，这也取决于当时随机过程的概率分布。首先，本文考虑了这类方程的温和解的存在唯一性。进一步，对该问题的弱解引入Trotter-Kato逼近系统，得到了诱导概率测度和零级逼近的弱收敛性.然后我们考虑了这类方程的参数依赖性的经典极限定理。最后，给出了一个随机偏微分方程的例子来说明我们的结果。
英文摘要：
Motivated by the work of T.E. Govindan in [5,8,9], this paper is concerned with a more general semilinear stochastic evolution equation. The difference between the equations considered in this paper and the previous one is that it makes some changes to the nonlinear function in random integral, which also depends on the probability distribution of stochastic process at that time. First, this paper considers the existence and uniqueness of mild solutions for such equations. Furthermore, Trotter-Kato approximation system is introduced for the mild solutions, and the weak convergence of induced probability measures and zeroth-order approximations are obtained. Then we consider the classical limit theorem about the parameter dependence of this kind of equations. Finally, an example of stochastic partial differential equation is given to illustrate our results.
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