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2017 Necessary and sufficient conditions for the $r$-excessive local martingales to be martingales
Mikhail Urusov, Mihail Zervos
Electron. Commun. Probab. 22: 1-6 (2017). DOI: 10.1214/17-ECP42

Abstract

We consider the decreasing and the increasing $r$-excessive functions $\varphi _r$ 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 $\bigl ( e^{-r (t \wedge T_\alpha )} \varphi _r (X_{t \wedge T_\alpha }) \bigr )$ $\bigl ($resp., $\bigl ( e^{-r (t \wedge T_\beta )} \psi _r (X_{t \wedge T_\beta }) \bigr ) \bigr )$ is a strict local martingale if the boundary point $\alpha $ (resp., $\beta $) is inaccessible and entrance, and a martingale otherwise.

Citation

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Mikhail Urusov. Mihail Zervos. "Necessary and sufficient conditions for the $r$-excessive local martingales to be martingales." Electron. Commun. Probab. 22 1 - 6, 2017. https://doi.org/10.1214/17-ECP42

Information

Received: 31 March 2016; Accepted: 12 January 2017; Published: 2017
First available in Project Euclid: 26 January 2017

zbMATH: 1357.60045
MathSciNet: MR3607805
Digital Object Identifier: 10.1214/17-ECP42

Subjects:
Primary: 60G44, 60G48, 60J60

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