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.