The Martingale Property in the Context of Stochastic Differential Equations

Abstract

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.

Revised version. Published in Electron. Commun. Probab

References in corpus (2)

• Equivalent and absolutely continuous measure changes for jump-diffusion processes
• Supermartingales as Radon-Nikodym densities and related measure extensions

Cited by in corpus (3)

• Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions
• Supermartingales as Radon-Nikodym densities and related measure extensions
• Symmetries of Stochastic Differential Equations using Girsanov transformations