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Quadratic Covariation and Itô's Formula for Smooth Nondegenerate Martingales

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Abstract

In this paper we prove the existence of the quadratic covariation [f(X),X], where f is a locally square integrable function and Xt = ∫t 0 u s dW s is a smooth nondegenerate Brownian martingale. This result is based on some moment estimates for Riemann sums which are established by means of the techniques of the Malliavin calculus.

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Authors
  1. S. Moret
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  2. D. Nualart
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Moret, S., Nualart, D. Quadratic Covariation and Itô's Formula for Smooth Nondegenerate Martingales. Journal of Theoretical Probability 13, 193–224 (2000). https://doi.org/10.1023/A:1007791027791

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