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August 2007 On Itô’s formula for elliptic diffusion processes
Xavier Bardina, Carles Rovira
Bernoulli 13(3): 820-830 (August 2007). DOI: 10.3150/07-BEJ6049


Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83–109] prove an extension of Itô’s formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303–328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.


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Xavier Bardina. Carles Rovira. "On Itô’s formula for elliptic diffusion processes." Bernoulli 13 (3) 820 - 830, August 2007.


Published: August 2007
First available in Project Euclid: 7 August 2007

zbMATH: 1133.60024
MathSciNet: MR2348752
Digital Object Identifier: 10.3150/07-BEJ6049

Keywords: Diffusion processes , integration with respect to local time , Itô’s formula , Local time

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability


Vol.13 • No. 3 • August 2007
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