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Stochastic integration with respect to q Brownian motion
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  • Published: January 2003

Stochastic integration with respect to q Brownian motion

  • C. Donati-Martin1 

Probability Theory and Related Fields volume 125, pages 77–95 (2003)Cite this article

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Abstract

 We develop a stochastic integration with respect to a q-Brownian motion (for ), i.e. a non commutative process where the operator a t and its adjoint fulfill the q commutation relation ; under the vacuum state expectation. We show that this process enjoys a predictable representation type property.

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Authors and Affiliations

  1. Laboratoire de Statistique et Probabilités, Univ. P. Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04, France. e-mail: donati@cict.fr, , , , , , FR

    C. Donati-Martin

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  1. C. Donati-Martin
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Additional information

Received: 15 February 2002 / Revised version: 25 May 2002 / Published online: 30 September 2002

Mathematics Subject Classification (2000): 60H05, 46L50, 81S25

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Cite this article

Donati-Martin, C. Stochastic integration with respect to q Brownian motion. Probab Theory Relat Fields 125, 77–95 (2003). https://doi.org/10.1007/s00440-002-0224-4

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  • Issue Date: January 2003

  • DOI: https://doi.org/10.1007/s00440-002-0224-4

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Keywords

  • Brownian Motion
  • Stochastic Integration
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