Integration with respect to local time and Itô’s
formula for smooth nondegenerate martingales
Xavier Bardina and Carles Rovira
Departament de Matemàtiques, Edifici C, Universitat Auṭnoma
de Barcelona
08193 Bellaterra, Barcelona, Spain
Facultat de Matemàtiques, Universitat de Barcelona, Gran
Via 585, 08007-Barcelona, Spain.
Abstract
We show an Itô’s formula for nondegenerate Brownian martingales and functions F(x, t) with locally integrable derivatives in t and x. We prove that one can express the additional term in Itô’s s formula as an integral over space and time with respect to local time.
Keywords: Martingales; Integration wrt local time; Itô's formula; Local time;
Published in: Publicacions Matemàtiques, 54 (1), 187-208, 2010.