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Journal of Theoretical Probability

, Volume 31, Issue 3, pp 1539–1589 | Cite as

Asymptotic Behavior of Weighted Power Variations of Fractional Brownian Motion in Brownian Time

  • Raghid Zeineddine
Article
  • 94 Downloads

Abstract

We study the asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time \(Z_t:= X_{Y_t},t \geqslant 0\), where X is a fractional Brownian motion and Y is an independent Brownian motion.

Keywords

Weighted power variations Limit theorem Malliavin calculus Fractional Brownian motion Fractional Brownian motion in Brownian time 

Mathematics Subject Classification 2010

60F05 60G15 60G22 60H05 60H07 

Notes

Acknowledgements

We are thankful to the referees for their careful reading of the original manuscript and for a number of suggestions. The financial support of the DFG (German Science Foundations) Research Training Group 2131 is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Research Training Group 2131, Fakultät MathematikTechnische Universität DortmundDortmundGermany

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