Laplace Symbols and Invariant Distributions

TL;DR

This paper introduces Laplace symbols for bounded Itô processes, linking them to generators, and derives an integral criterion for invariant distributions, with some applications discussed.

Contribution

It presents a novel Laplace symbol concept for bounded Itô processes and establishes a new integral criterion for invariant distributions.

Findings

Laplace symbols are connected to infinitesimal generators.

An integral criterion for invariant distributions is derived.

Applications of the theory are discussed.

Abstract

We introduce a new kind of symbol in the framework of It\^o processes which are bounded on one side. The connection between this symbol and the infinitesimal generator is analyzed. Based on this concept, an integral criterion for invariant distributions of the underlying process is derived. Some applications are mentioned.