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

2008/03/25 by Xavier Bardina, Bardina, Xavier, Carles Rovira +1
Mathematics · #60H05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H05

paper · pdf · doi:10.48550/arxiv.0803.3522

arxiv created 2008/03/25 · arxiv updated 2009/12/01

Abstract

We show an It\^ o's formula for nondegenerate Brownian martingales X_t=∫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.

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