Título:
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On Ito's formula for elliptic diffusion processes
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Autor/a:
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Bardina i Simorra, Xavier; Rovira Escofet, Carles
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Otros autores:
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Universitat de Barcelona |
Abstract:
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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. |
Materia(s):
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-Integrals estocàstiques -Anàlisi estocàstica -Integrals estocàstiques -Stochastic analysis |
Derechos:
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(c) ISI/BS, International Statistical Institute, Bernoulli Society, 2007
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Tipo de documento:
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Artículo Artículo - Versión publicada |
Editor:
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Bernoulli Society for Mathematical Statistics and Probability
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