Existence of probability measure valued jump-diffusions in generalized Wasserstein spaces
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 proble...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
21.08.2019
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.48550/arxiv.1908.08080 |