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Information-equivalence: On Filtrations Created by Independent Increments

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

Abstract

This article investigates filtrations created by the increments-processes of processes with independent increments: Suppose two processes create the same filtrations, when will the processes of their increments also create the same filtrations?

Our main result is that the processes of increments of two extremal continuous martingales with independent increments create the same filtrations if and only if either process admits a deterministic representation with respect to the other.

Keywords

  • Brownian Motion
  • Polish Group
  • Standard Brownian Motion
  • Independent Increment
  • Stationary Increment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Hans Bühler .

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© 2005 Springer-Verlag Berlin/Heidelberg

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Bühler, H. (2005). Information-equivalence: On Filtrations Created by Independent Increments. 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_14

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