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2020 Semimartingales on duals of nuclear spaces
Christian A. Fonseca-Mora
Electron. J. Probab. 25: 1-24 (2020). DOI: 10.1214/20-EJP444


This work is devoted to the study of semimartingales on the dual of a general nuclear space. We start by establishing conditions for a cylindrical semimartingale in the strong dual $\Phi '$ of a nuclear space $\Phi $ to have a $\Phi '$-valued semimartingale version whose paths are right-continuous with left limits. Results of similar nature but for more specific classes of cylindrical semimartingales and examples are also provided. Later, we will show that under some general conditions every semimartingale taking values in the dual of a nuclear space has a canonical representation. The concept of predictable characteristics is introduced and is used to establish necessary and sufficient conditions for a $\Phi '$-valued semimartingale to be a $\Phi '$-valued Lévy process.


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Christian A. Fonseca-Mora. "Semimartingales on duals of nuclear spaces." Electron. J. Probab. 25 1 - 24, 2020.


Received: 14 March 2019; Accepted: 6 March 2020; Published: 2020
First available in Project Euclid: 26 March 2020

zbMATH: 1445.60037
MathSciNet: MR4089786
Digital Object Identifier: 10.1214/20-EJP444

Primary: 60B11 , 60G17 , 60G20 , 60G48

Keywords: cylindrical semimartingales , dual of a nuclear space , Lévy processes , regularization theorem , semimartingale canonical representation , Semimartingales


Vol.25 • 2020
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