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Simple examples of non-generating Girsanov processes

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Book cover Séminaire de Probabilités XXXI

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1655))

Abstract

Let B(t), 0≤t≤∞ be a Brownian motion on (ω, F, P) with with B 0=0. Let F(t), 0≤t≤∞ be its filtration, with F(∞)=F. We construct, simple examples of probability measures P′≈P for which this filtration is not generated by the corresponding Girsanov process, but is nevertheless generated by some process which is a Brownian motion for the measure P′.

Supported in part by NSF Grant #DMS 9113642

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References

  • [DFST] L. Dubins, J. Feldman, M. Smorodinsky, and B.S. Tsirelson (1995): Decreasing sequences of ∂-fields and a measure change for Brownian motion, to appear, Ann. Prob.

    Google Scholar 

  • [K] N. Kazamaki (1994): Continuous exponential martingales and BMO, Lec. Notes Math. 1579, Springer-Verlag.

    Google Scholar 

  • [R] M. Rosenblatt (1959): Stationary processes as shifts of functions of independent random variables, Jour. Math. Mech. 8, pp. 665–681.

    MathSciNet  MATH  Google Scholar 

  • [RY] D. Revuz, and M. Yor (1991): Continuous Martingales and Brownian Motion, Springer, Berlin.

    Book  MATH  Google Scholar 

  • [T] B. S. Tsirelson, (1975): An example of a stochastic differential equation having no strong solution, Theor. Prob. Appl. 20, pp. 416–418.

    Article  Google Scholar 

  • [V] A. M. Vershik, (1994): Theory of decreasing sequences of measurable partitions, Alg. Anal. 6, pp. 1–68 in Russian; English version to appear in St. Petersburg Math. Jour. 6.

    MathSciNet  MATH  Google Scholar 

  • [Y] M. Yor, (1992): Tsirelson’s equation in discrete time Prob. Th. Related Fields, 91, pp. 135–152.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. University of California, Berkeley

    J. Feldman & M. Smorodinsky

  2. Tel-Aviv University, Tel-Aviv, Israel

    J. Feldman & M. Smorodinsky

Authors
  1. J. Feldman
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  2. M. Smorodinsky
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Jacques Azéma Marc Yor Michel Emery

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© 1997 Springer-Verlag Berlin Heidelberg

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Feldman, J., Smorodinsky, M. (1997). Simple examples of non-generating Girsanov processes. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119309

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  • DOI: https://doi.org/10.1007/BFb0119309

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62634-3

  • Online ISBN: 978-3-540-68352-0

  • eBook Packages: Springer Book Archive

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