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2020 On uniqueness of solutions to martingale problems — counterexamples and sufficient criteria
Jan Kallsen, Paul Krühner
Electron. J. Probab. 25: 1-33 (2020). DOI: 10.1214/20-EJP494

Abstract

The dynamics of a Markov process are often specified by its infinitesimal generator or, equivalently, its symbol. This paper contains examples of analytic symbols which do not determine the law of the corresponding Markov process uniquely. These examples also show that the law of a polynomial process in the sense of [4, 5, 11] is not necessarily determined by its generator if it has jumps. On the other hand, we show that a combination of smoothness of the symbol and ellipticity warrants uniqueness in law. The proof of this result is based on proving stability of univariate marginals relative to some properly chosen distance.

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Jan Kallsen. Paul Krühner. "On uniqueness of solutions to martingale problems — counterexamples and sufficient criteria." Electron. J. Probab. 25 1 - 33, 2020. https://doi.org/10.1214/20-EJP494

Information

Received: 8 May 2019; Accepted: 4 July 2020; Published: 2020
First available in Project Euclid: 13 August 2020

zbMATH: 07252727
MathSciNet: MR4136475
Digital Object Identifier: 10.1214/20-EJP494

Subjects:
Primary: 47G30 , 60J35 , 60J75

Keywords: Jump processes , Markov process , Martingale problem , polynomial process , ‎pseudo-differential operator , symbol , uniqueness

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