Open Access
February 2020 The fourth characteristic of a semimartingale
Alexander Schnurr
Bernoulli 26(1): 642-663 (February 2020). DOI: 10.3150/19-BEJ1145


We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space $\mathbb{R}^{d}$. In particular, Markov processes related to sub-Markovian kernels, but also non-Markovian processes with path-dependent behavior. By carefully distinguishing between two killing states, we are able to introduce a fourth semimartingale characteristic which generalizes the fourth part of the Lévy quadruple. Using the probabilistic symbol, we analyze the close relationship between the generators of certain Markov processes with killing and their (now four) semimartingale characteristics.


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Alexander Schnurr. "The fourth characteristic of a semimartingale." Bernoulli 26 (1) 642 - 663, February 2020.


Received: 1 August 2018; Revised: 1 July 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140512
MathSciNet: MR4036047
Digital Object Identifier: 10.3150/19-BEJ1145

Keywords: killing , Markov process , Semimartingale , symbol

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 1 • February 2020
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