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

Xavier Bardina; Carles Rovira

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

Probability 2008-03-26 v1

Authors: Xavier Bardina , Carles Rovira

Abstract

We show an It\^ o'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 It\^o's s formula as an integral over space and time with respect to local time.

Keywords

local time Itô formula nondegenerate martingale Brownian martingale stochastic integration

Cite

@article{arxiv.0803.3522,
  title  = {Integration with respect to local time and Ito's formula for smooth nondegenerate martingales},
  author = {Xavier Bardina and Carles Rovira},
  journal= {arXiv preprint arXiv:0803.3522},
  year   = {2008}
}

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