On uniqueness of solutions to martingale problems --- counterexamples and sufficient criteria



Kallsen, Jan and Krühner, Paul
(2020) On uniqueness of solutions to martingale problems --- counterexamples and sufficient criteria. Electronic Journal of Probability, 25.

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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.

Item Type: Article
Uncontrolled Keywords: math.PR, math.PR, 47G30, 60J35, 60J75
Depositing User: Symplectic Admin
Date Deposited: 25 Sep 2020 07:36
Last Modified: 09 Jan 2021 01:28
DOI: 10.1214/20-EJP494
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3102426