Green Measures for Markov Processes
Yuri G. Kondratiev, Jos\'e L. da Silva
TL;DR
This paper investigates Green measures for specific Markov processes, including Brownian motion and jump processes, providing a representation that separates singular and regular parts and addressing bounds for the regular component.
Contribution
It introduces a novel representation of Green measures for Markov processes, decomposing them into singular and regular parts and establishing bounds for the regular part.
Findings
Representation of Green measures as sum of singular and regular parts
Bound for the regular part of Green measures
Application to Brownian motion and jump processes
Abstract
In this paper we study Green measures of certain classes of Markov processes. In particular Brownian motion and processes with jump generators with different tails. The Green measures are represented as a sum of a singular and a regular part given in terms of the jump generator. The main technical question is to find a bound for the regular part.
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