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2020 Existence of probability measure valued jump-diffusions in generalized Wasserstein spaces
Martin Larsson, Sara Svaluto-Ferro
Electron. J. Probab. 25: 1-25 (2020). DOI: 10.1214/20-EJP562


We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of probability measures into locally compact spaces where classical existence theory for martingale problems can be applied. The method allows for general dynamics including drift, diffusion, and possibly infinite-activity jumps. We also develop tools for verifying the required conditions on the generator, including the positive maximum principle and certain continuity and growth conditions. To illustrate the abstract results, we consider large particle systems with mean-field interaction and common noise.


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Martin Larsson. Sara Svaluto-Ferro. "Existence of probability measure valued jump-diffusions in generalized Wasserstein spaces." Electron. J. Probab. 25 1 - 25, 2020.


Received: 22 August 2019; Accepted: 29 November 2020; Published: 2020
First available in Project Euclid: 24 December 2020

Digital Object Identifier: 10.1214/20-EJP562

Primary: 60G57, 60J60, 60J75


Vol.25 • 2020
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