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On Ito's formula for elliptic diffusion processes
Bardina i Simorra, Xavier; Rovira Escofet, Carles
Universitat de Barcelona
Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito'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.
2012-04-18
Integrals estocàstiques
Anàlisi estocàstica
Integrals estocàstiques
Stochastic analysis
(c) ISI/BS, International Statistical Institute, Bernoulli Society, 2007
Article
Bernoulli Society for Mathematical Statistics and Probability
         

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