On Itô's formula for multidimensional Brownian motion

Arbeitspapier

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 373 Discussion Paper ; No. 2001,90

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: Ito's formula ; Brownian motion ; stochastic integrals ; quadratic covariation ; Dirichlet spaces ; polar sets

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Föllmer, Hans ; Protter, Philip E.
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (wo): Berlin
• (wann): 2001

Weitere Informationen

• Handle: http://hdl.handle.net/10419/62732
• URN: urn:nbn:de:kobv:11-10051072
• Letzte Aktualisierung: 10.03.2025, 11:41 MEZ