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The Martingale Property in the Context of Stochastic Differential Equations

Published 2013-06-02, updated 2015-04-26Version 2

This note studies the martingale property of a nonnegative, continuous local martingale Z, given as a nonanticipative functional of a solution to a stochastic differential equation. The condition states that Z is a (uniformly integrable) martingale if and only if an integral test of a related functional holds.

Comments: Revised version. Published in Electron. Commun. Probab

Journal: Electron. Commun. Probab. 20 (2015), no. 34, 1-10

DOI: 10.1214/ECP.v20-3449

Categories: math.PR

Keywords: stochastic differential equations, martingale property, integral test, martingale problem, nonnegative local martingale

Tags: journal article

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