The martingale property in the context of stochastic differential equations

2013/06/30 by Johannes Ruf · 1 citation
Economics, Econometrics and Finance · Mathematics · #Doob's martingale inequality #Economic theories and models #Local martingale #Martingale (probability theory) #Martingale difference sequence #Martingale pricing #Martingale representation theorem #Nonlinear Differential Equations Analysis #Stochastic differential equation #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.1214/ecp.v20-3449

published as Electron. Commun. Probab. 20 (2015), no. 34, 1-10 · Revised version. Published in Electron. Commun. Probab

openalex publication_date 2015/01/01 · arxiv created 2015/04/26 · arxiv updated 2015/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Equivalent and absolutely continuous measure changes for jump-diffusion processes

Cited by

• Symmetries of stochastic differential equations using Girsanov transformations