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A connection between the expansion of filtrations and Girsanov's theorem

Part of the Lecture Notes in Mathematics book series (LNM,volume 1390)

Abstract

We give sufficient conditions under which a continuous local martingale remains a continuous local martingale under a simultaneous initial expansion of the filtration of σ-fields and change to an equivalent probability law. In particular this gives a method for a Brownian motion to remain a Brownian motion under such a double transformation. The classical example of K. Itô is treated in detail.

Key words and phrases

  • Brownian motion
  • local martingale
  • semimartingale
  • initial expansion of filtrations
  • Girsanov's theorem

Supported in part by NSF Grant # 8500997

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References

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© 1989 Springer-Verlag

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Protter, P. (1989). A connection between the expansion of filtrations and Girsanov's theorem. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications II. Lecture Notes in Mathematics, vol 1390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083949

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  • DOI: https://doi.org/10.1007/BFb0083949

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51510-4

  • Online ISBN: 978-3-540-48200-0

  • eBook Packages: Springer Book Archive