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2018 On martingale problems and Feller processes
Franziska Kühn
Electron. J. Probab. 23: 1-18 (2018). DOI: 10.1214/18-EJP142

Abstract

Let $A$ be a pseudo-differential operator with negative definite symbol $q$. In this paper we establish a sufficient condition such that the well-posedness of the $(A,C_c^{\infty }(\mathbb{R} ^d))$-martingale problem implies that the unique solution to the martingale problem is a Feller process. This provides a proof of a former claim by van Casteren. As an application we prove new existence and uniqueness results for Lévy-driven stochastic differential equations and stable-like processes with unbounded coefficients.

Citation

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Franziska Kühn. "On martingale problems and Feller processes." Electron. J. Probab. 23 1 - 18, 2018. https://doi.org/10.1214/18-EJP142

Information

Received: 4 September 2017; Accepted: 15 January 2018; Published: 2018
First available in Project Euclid: 12 February 2018

zbMATH: 1390.60278
MathSciNet: MR3771750
Digital Object Identifier: 10.1214/18-EJP142

Subjects:
Primary: 60J25
Secondary: 60G44, 60G51, 60H10, 60J75

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Vol.23 • 2018
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