Open Access
2009 An optimal Itô formula for Lévy processes
Nathalie Eisenbaum, Alexander Walsh
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Electron. Commun. Probab. 14: 202-209 (2009). DOI: 10.1214/ECP.v14-1469


Several Itô formulas have been already established for Lévy processes. We explain according to which criteria they are not optimal and establish an extended Itô formula that satisfies that criteria. The interest, in particular, of this formula is to obtain the explicit decomposition of $F(X)$, for $X$ Lévy process and $F$ deterministic function with locally bounded first order Radon-Nikodym derivatives, as the sum of a Dirichlet process and a bounded variation process.


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Nathalie Eisenbaum. Alexander Walsh. "An optimal Itô formula for Lévy processes." Electron. Commun. Probab. 14 202 - 209, 2009.


Accepted: 24 April 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1191.60058
MathSciNet: MR2507749
Digital Object Identifier: 10.1214/ECP.v14-1469

Primary: 60G44
Secondary: 60H05 , 60J55 , 60J65

Keywords: Itô formula , Lévy process , Local time , stochastic calculus

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