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Integration with respect to local time and Itô's formula for smooth nondegenerate martingales

Xavier Bardina and Carles Rovira

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We show an Itô's formula for nondegenerate Brownian martingales $X_t=\int_0^t u_s \,dW_s$ 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.

Article information

Publ. Mat., Volume 54, Number 1 (2010), 187-208.

First available in Project Euclid: 8 January 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H05: Stochastic integrals 60G44: Martingales with continuous parameter

Martingales integration wrt local time Itô's formula local time


Bardina, Xavier; Rovira, Carles. Integration with respect to local time and Itô's formula for smooth nondegenerate martingales. Publ. Mat. 54 (2010), no. 1, 187--208.

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