The Martingale Problem Method Revisited

2021/08/26 by David Criens, Criens, David, Peter Pfaffelhuber +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2108.11930

openalex publication_date 2021/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 cadlag 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.

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