Lévy bases on manifolds
Pub. online: 4 November 2026
Type: Research Article
Open Access
Open Access
Received
27 April 2026
27 April 2026
Accepted
16 October 2026
16 October 2026
Published
4 November 2026
4 November 2026
Abstract
This paper studies Lévy bases on Riemannian manifolds and related processes built from them. We argue that the canonical choice of intensity measure is the Riemannian measure on the manifold, and show how this allows for transporting properties of Lévy bases on ${\mathbb{R}^{d}}$ to the manifold setting via metatimes and subordination constructions. We show how this links to time-changed Lévy processes and how to naturally extend the setting to manifolds with (possibly stochastically) evolving metrics via generalized time-changes. As applications, we introduce so-called M-trawl processes, which generalize the classical trawl processes by letting the trawl operation be induced by a geometric flow, and we discuss the interpretation of Lévy bases on manifolds as Lévy white noise for stochastic partial differential equations on manifolds with Lévy-type forcing.
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