We study boundary value problems involving non-local operators for the dynamic boundary conditions. Our analysis includes a detailed description of such operators together with their relations with random times and random functionals. We provide some new characterizations for the boundary behaviour of the Brownian motion based on the interplay between non-local operators and boundary value problems.

In this paper we deal with some open problems concerned with Gamma subordinators. In particular, we first provide a representation for the moments of the inverse gamma subordinator. Then, we focus on k-potentials and we study the governing equations associated with Gamma subordinators and inverse processes. Such representations are given in terms of higher transcendental functions, also known as Volterra functions.

In this paper we deal with some open problems concerned with gamma subordinators. In particular, we provide a representation for the moments of the inverse gamma subordinator. Then, we focus on λ-potentials and we study the governing equations associated with gamma subordinators and inverse processes. Such representations are given in terms of higher transcendental functions, also known as Volterra functions