The generalized covariation process and Ito formula

Ito Formula for an Asymptotically 4-stable Process Krzysztof Burdzy

An Itô-type formula is given for an asymptotically 4-stable process.

A proof of Ito ' s formula using a discrete Ito ' s formula

Generalized covariation for Banach space valued processes, Itô formula and applications

This paper discusses a new notion of quadratic variation and covariation for Banach space valued processes (not necessarily semimartingales) and related Itô formula. If X and Y take respectively values in Banach spaces B1 and B2 and χ is a suitable subspace of the dual of the projective tensor product of B1 and B2 (denoted by (B1⊗̂πB2) ), we define the so-called χ-covariation of X and Y. If X = ...

Generalized covariation and extended Fukushima decompositions

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of Métivier and Pellaumail which is quite restrictive. We make use of the notion of χ-covariation which is a generalized notion of covariation for processes with values in two Banach spaces B1 and B2. χ refers to a suitable subspace of the dual ...

Ito formula for the infinite dimensional fractional Brownian motion

We introduce the stochastic integration with respect to the infinite-dimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an Itô formula for Hurst parameter bigger than 1 2 .