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2001 Finitely Polynomially Determined Lévy Processes
Arindam Sengupta, Anish Sarkar
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Electron. J. Probab. 6: 1-22 (2001). DOI: 10.1214/EJP.v6-80


A time-space harmonic polynomial for a continuous-time process $X=\{X_t : t \ge 0\} $ is a two-variable polynomial $ P $ such that $ \{ P(t,X_t) : t \ge 0 \} $ is a martingale for the natural filtration of $ X $. Motivated by Lévy's characterisation of Brownian motion and Watanabe's characterisation of the Poisson process, we look for classes of processes with reasonably general path properties in which a characterisation of those members whose laws are determined by a finite number of such polynomials is available. We exhibit two classes of processes, the first containing the Lévy processes, and the second a more general class of additive processes, with this property and describe the respective characterisations.


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Arindam Sengupta. Anish Sarkar. "Finitely Polynomially Determined Lévy Processes." Electron. J. Probab. 6 1 - 22, 2001.


Accepted: 30 August 2000; Published: 2001
First available in Project Euclid: 19 April 2016

zbMATH: 0974.60026
MathSciNet: MR1831802
Digital Object Identifier: 10.1214/EJP.v6-80

Primary: 60G44
Secondary: 60J30

Keywords: additive process , Kolmogorov measure , Lévy measure , Lévy process , Lévy's characterisation

Vol.6 • 2001
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