Open Access
2023 The martingale problem method revisited
David Criens, Peter Pfaffelhuber, Thorsten Schmidt
Author Affiliations +
Electron. J. Probab. 28: 1-46 (2023). DOI: 10.1214/23-EJP902


We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales), nor to continuous or càdlàg paths. We illustrate our findings both, by finding generalizations of known results, and proving new results. For the latter, we work on processes with fixed times of discontinuity.

Funding Statement

DC acknowledges financial support from the DFG project No. SCHM 2160/15-1.


The authors are grateful to an anonymous referee for many helpful comments and suggestions. DC acknowledges financial support from the DFG project No. SCHM 2160/15-1.


Download Citation

David Criens. Peter Pfaffelhuber. Thorsten Schmidt. "The martingale problem method revisited." Electron. J. Probab. 28 1 - 46, 2023.


Received: 26 August 2021; Accepted: 11 January 2023; Published: 2023
First available in Project Euclid: 8 February 2023

MathSciNet: MR4546023
zbMATH: 07707111
Digital Object Identifier: 10.1214/23-EJP902

Primary: 60G07
Secondary: 60F17 , 60G17 , 60H15

Keywords: fixed times of discontinuity , limit theorems , local uniform topology , Martingale problem , path space , Semimartingales , Skorokhod topology , stable convergence , Volterra equations , weak-strong convergence

Vol.28 • 2023
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