Generalized covariation for Banach space valued processes, Itō formula and applications (Q470098)

The paper discusses the theory and applications of ``quadratic variation'' and ``covariation'' for stochastic processes defined in Banach spaces. The covariation of two processes is defined by means of the covariance of their increments, and the quadratic variation of a process is the covariance of the latter with itself. A window process takes on values in the non-reflexive Banach space of real continuous functions defined on \((-a,0)\), \(0<a<T\).NEWLINENEWLINE The paper displays the theoretical basis to develop a stochastic calculus which starts from these concepts. The authors study \(\chi\)-covariation and \(\chi\)-quadratic variation, and then develop the calculations related to window processes. Then Itō's formula for windows is derived, and some illustrative examples are given.