an:07252727
Zbl 07252727
Kallsen, Jan; Kr??hner, Paul
On uniqueness of solutions to martingale problems -- counterexamples and sufficient criteria
EN
Electron. J. Probab. 25, Paper No. 95, 33 p. (2020).
00443788
2020
j
47G30 60J35 60J75
symbol; martingale problem; uniqueness; polynomial process; Markov process; pseudo-differential operator; jump processes
Summary: 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.