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Erscheinungsjahr: 
2001
Schriftenreihe/Nr.: 
SFB 373 Discussion Paper No. 2001,90
Verlag: 
Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, Berlin
Zusammenfassung: 
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.
Schlagwörter: 
Ito's formula
Brownian motion
stochastic integrals
quadratic covariation
Dirichlet spaces
polar sets
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Dokumentart: 
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