论文标题
非线性扩散的Markov选择和伐木特性
Markov selections and Feller properties of nonlinear diffusions
论文作者
论文摘要
在本文中，我们研究了一个非线性（条件）期望的家族，可以理解为具有不确定局部特征的扩散。在这里，差异特性由设置值函数规定。我们建立了其捕获物的特性，并检查如何线性化相关的sublinear马尔可夫半群。特别是，我们观察到具有足够随机性的框架中均方根半群的新型平滑效果。此外，我们将与半群相对应的值函数与非线性kolmogorov方程联系起来。这提供了与所谓的Nisio Semigroup的联系。
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a diffusion with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function. We establish its Feller properties and examine how to linearize the associated sublinear Markovian semigroup. In particular, we observe a novel smoothing effect of sublinear semigroups in frameworks which carry enough randomness. Furthermore, we link the value function corresponding to the semigroup to a nonlinear Kolmogorov equation. This provides a connection to the so-called Nisio semigroup.
