---
abstract: 'Starting from the seventies mathematicians face the question whether a non-negative local martingale is a true or a strict local martingale. In this article we answer this question from a semimartingale perspective. We connect the martingale property to existence, uniqueness and topological properties of semimartingale problems. This not only leads to valuable characterizations of the martingale property, but also reveals new existence and uniqueness results for semimartingale problems. As a case study we derive explicit conditions for the martingale property of stochastic exponentials driven by infinite-dimensional Brownian motion.'
address:
- 'D. Criens - Technical University of Munich, Center for Mathematics, Germany'
- 'K. Glau - Technical University of Munich, Center for Mathematics, Germany'
author:
- David Criens
- Kathrin Glau
bibliography:
- 'References.bib'
title: Martingale Property in Terms of Semimartingale Problems
---

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True or Strict Local Martingale
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Introduction
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The question whether a non-negative local martingale is a strict local or a true martingale is of fundamental probabilistic nature. It relates to existence of solutions to stochastic differential equations and martingale problems, as well as to absolute continuity of laws.

