Electronic Communications in Probability

The martingale property in the context of stochastic differential equations

Johannes Ruf

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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.

Article information

Electron. Commun. Probab., Volume 20 (2015), paper no. 34, 10 pp.

Accepted: 25 April 2015
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G44: Martingales with continuous parameter
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Test of martingale property local martingale integral test Föllmer measure

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Ruf, Johannes. The martingale property in the context of stochastic differential equations. Electron. Commun. Probab. 20 (2015), paper no. 34, 10 pp. doi:10.1214/ECP.v20-3449. https://projecteuclid.org/euclid.ecp/1465320961

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