Stable processes with stationary increments parameterized by metric spaces

Abstract

A new family of stable processes indexed by metric spaces with stationary increments are introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a result on the so-called measure definite kernels is of independent interest. A limit theorem for set-indexed processes is also established.

16 pages, minor revision

References in corpus (2)

• A generalisation of the fractional Brownian field based on non-Euclidean norms
• On the existence of fractional Brownian fields indexed by manifolds with closed geodesics