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Positive Bilinear Mappings Associated with Stochastic Processes

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1857)

Abstract

On some vector spaces of adapted stochastic processes, we define increasing families of positive bilinear forms, which generalize the usual square brackets [X,Y] and angle brackets \({\langle X,Y\rangle}\). We study the corresponding Hardy spaces especially for p = 1 or 2, and extend to this abstract framework results of Fefferman type from martingale theory.

Keywords

  • Hardy Space
  • Countable Union
  • Local Martingale
  • Angle Bracket
  • Martingale Theory

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Correspondence to Valentin Grecea .

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© 2005 Springer-Verlag Berlin/Heidelberg

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Grecea, V. (2005). Positive Bilinear Mappings Associated with Stochastic Processes. In: Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVIII. Lecture Notes in Mathematics, vol 1857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31449-3_10

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