Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/62732
Authors: 
Föllmer, Hans
Protter, Philip E.
Year of Publication: 
2001
Series/Report no.: 
Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 2001,90
Abstract: 
Consider a d-dimensional Brownian motion X (Xl, ... ,Xd ) and a function F which belongs locally to the Sobolev space W 1,2. We prove an extension of Ito's formula where the usual second order terms are replaced by the quadratic covariations [fk(X), Xkj involving the weak first partial derivatives fk of F. In particular we show that for any locally square-integrable function f the quadratic covariations [f(X), Xkj exist as limits in probability for any starting point, except for some polar set. The proof is based on new approximation results for forward and backward stochastic integrals.
Subjects: 
Ito's formula
Brownian motion
stochastic integrals
quadratic covariation
Dirichlet spaces
polar sets
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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