求解具有无界非线性扰动的随机方程
Solving stochastic equations with unbounded nonlinear perturbations
摘要：
本文研究了在确定性部分和/或随机部分具有无界非线性扰动的半线性随机方程。此外，这些方程的线性部分由不一定解析的半群支配。这些方程的主要困难是如何定义的概念温和的解决方案，由于所选择的类型的无界扰动。为了克服这个问题，我们首先证明了随机卷积关于“容许”无界线性算子（不一定是封闭的或可封闭的）的域的正则性。这是使用Yosida扩展这样的无界线性算子。在证明了这些方程的适定性之后，我们还建立了相应的转移半群的Feller性质。给出了热方程和薛定谔方程等几个具有非局部扰动项的例子。最后，我们给出了一类半线性中立型随机方程的应用。
英文摘要：
This paper is interested in semilinear stochastic equations having unbounded nonlinear perturbations in the deterministic part and/or in the random part. Moreover, the linear part of these equations is governed by a not necessarily analytic semigroup. The main difficulty with these equations is how to define the concept of mild solutions due to the chosen type of unbounded perturbations. To overcome this problem, we first proved a regularity property of the stochastic convolution with respect to the domain of "admissible" unbounded linear operators (not necessarily closed or closable). This is done using Yosida extensions of such unbounded linear operators. After proving the well-posedness of these equations, we also establish the Feller property for the corresponding transition semigroups. Several examples like heat equations and schrödinger equations with nonlocal perturbations terms are given. Finally, we give an application to a general class of semilinear neutral stochastic equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
