Local time-space stochastic calculus for Lévy processes

Nathalie Eisenbaum

Stochastic Processes and their Applications, 2006, vol. 116, issue 5, 757-778

Abstract: We develop a stochastic calculus on the plane with respect to the local times of a large class of Lévy processes. We can then extend to these Lévy processes an Itô formula that was established previously for Brownian motion. Our method provides also a multidimensional version of the formula. We show that this formula generates many "Itô formulas" that fit various problems. In the special case of a linear Brownian motion, we recover a recently established Itô formula that involves local times on curves. This formula is already used in financial mathematics.

Keywords: Lévy; processes; Stochastic; calculus; Local; time; Ito; formula (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (5)

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