Titel
Existence of probability measure valued jump-diffusions in generalized Wasserstein spaces
Autor*in
Martin Larsson
Department of Mathematical Sciences, Carnegie Mellon University
Abstract
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.
Stichwort
Martingale problemMcKean–Vlasov equationspositive maximum principleprobability measure valued processesWasserstein spaces
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Electronic Journal of Probability
Band
25
ISSN
1083-6489
Erscheinungsdatum
2020
Publication
Institute of Mathematical Statistics
Erscheinungsdatum
2020
Zugänglichkeit
Rechte
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