Local time-space stochastic calculus for Lévy processes

DOI10.1016/j.spa.2005.12.002zbMath1114.60044OpenAlexW2049098836MaRDI QIDQ2495381

Nathalie Eisenbaum

Publication date: 30 June 2006

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2005.12.002

zbMATH Keywords

Lévy processesItô formulaBrownian componentlocal times on curvesvariant of stochastic calculus

Mathematics Subject Classification ID

Stochastic integrals (60H05) Local time and additive functionals (60J55)

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Cites Work

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• Time reversal on Lévy processes
• General change of variable formulas for semimartingales in one and finite dimensions
• Itô's formula for \(C^{1,\lambda}\)-functions of a càdlàg process and related calculus
• Integration with respect to local time
• Quadratic covariation and an extension of Itô's formula
• Ito formula for \(C^ 1\)-functions of semimartingales
• Finite expiry Russian options
• A change-of-variable formula with local time on curves
• CALLABLE PUTS AS COMPOSITE EXOTIC OPTIONS
• ON THE AMERICAN OPTION PROBLEM

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