Journal of Theoretical Probability

, Volume 13, Issue 1, pp 193–224 | Cite as

Quadratic Covariation and Itô's Formula for Smooth Nondegenerate Martingales

  • S. Moret
  • D. Nualart


In this paper we prove the existence of the quadratic covariation [f(X),X], where f is a locally square integrable function and Xt = ∫t0usdWs 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.

Itô's formula Malliavin calculus quadratic covariation 


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© Plenum Publishing Corporation 2000

Authors and Affiliations

  • S. Moret
  • D. Nualart

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