Necessary and sufficient conditions for the r-excessive local martingales to be martingales

作者：Urusov Mikhail^*; Zervos Mihail

来源：Electronic Communications in Probability, 2017, 22(0).

DOI：10.1214/17-ECP42

• one-dimensional strong Markov processes
• r-excessive functions
• local martingales

We consider the decreasing and the increasing r-excessive functions phi(r) and psi(r) that are associated with a one-dimensional conservative regular continuous strong Markov process X with values in an interval with endpoints alpha < beta. We prove that the r-excessive local martingale (e(-r( t <^>T alpha)) phi(r) (X (t <^> T alpha))) (resp., (e(-r(t <^>T beta)) psi(r) (X-t<^>T beta)) is a strict local martingale if the boundary point alpha (resp., beta) is inaccessible and entrance, and a martingale otherwise.

• 出版日期2017