Feller Generators with measurable lower order terms

TL;DR

This paper investigates how adding measurable lower order terms to Feller generators affects key properties like positivity and conservativeness, with implications for martingale problems and SDEs.

Contribution

It provides conditions under which properties of Feller semigroups are preserved under perturbations with measurable lower order terms.

Findings

Preservation of positivity and conservativeness under certain conditions

Examples illustrating the impact of lower order terms

Applications to martingale problems and SDEs with measurable coefficients

Abstract

We study perturbations of Feller generators under `lower order terms' with measurable coefficients. We investigate which properties of the original semigroup -- such as positivity, conservativeness and the Feller property -- are passed to the perturbed semigroup. We give several examples and discuss applications in the theory of martingale problems and stochastic differential equations with measurable coefficients.