A new technique for proving uniqueness for martingale problems

TL;DR

This paper introduces a novel technique for establishing the uniqueness of solutions to martingale problems, demonstrated through elliptic diffusions in multi-dimensional space.

Contribution

It presents a new method for proving uniqueness in martingale problems, expanding the toolkit for stochastic analysis.

Findings

Successfully proves uniqueness for elliptic diffusions.

Provides a general framework applicable to other martingale problems.

Enhances understanding of stochastic differential equations.

Abstract

A new technique for proving uniqueness of martingale problems is introduced. The method is illustrated in the context of elliptic diffusions in $R^d$.