Motivated by the notion of isotropic \(\alpha \)-stable Lévy processes confined, by reflections, to a bounded open Lipschitz set \(D\subset \mathbb {R}^d\), we study some related analytical objects. Thus, we construct the corresponding transition semigroup, identify its generator and prove exponential speed of convergence of the semigroup to a unique stationary distribution for large time.

中文翻译：

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带反射的分数拉普拉斯算子

受各向同性\(\alpha \) -稳定 Lévy 过程的概念的启发，通过反射限制到有界开放 Lipschitz 集\(D\subset \mathbb {R}^d\)，我们研究了一些相关的分析对象。因此，我们构造了相应的转移半群，识别了它的生成器并证明了半群在长时间内收敛到唯一平稳分布的指数速度。