Generalization of Itô's formula for smooth nondegenerate martingales

S. Moret and D. Nualart

Stochastic Processes and their Applications, 2001, vol. 91, issue 1, 115-149

Abstract: In this paper we prove the existence of the quadratic covariation [([not partial differential]F/[not partial differential]xk)(X), Xk] for all 1[less-than-or-equals, slant]k[less-than-or-equals, slant]d, where F belongs locally to the Sobolev space for some p>d and X is a d-dimensional smooth nondegenerate martingale adapted to a d-dimensional Brownian motion. This result is based on some moment estimates for Riemann sums which are established by means of the techniques of the Malliavin calculus. As a consequence we obtain an extension of Itô's formula where the complementary term is one-half the sum of the quadratic covariations above.

Keywords: Ito's; formula; Malliavin; calculus; Quadratic; covariation (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (1)

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