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Journal of Theoretical Probability

, Volume 29, Issue 3, pp 941–957 | Cite as

A first-order limit law for functionals of two independent fractional Brownian motions in the critical case

  • Junna Bi
  • Fangjun Xu
Article
  • 578 Downloads

Abstract

We prove a first-order limit law for functionals of two independent \(d\)-dimensional fractional Brownian motions with the same Hurst index \(H=2/d\,(d\ge 4)\), using the method of moments and extending a result by LeGall in the case of Brownian motion.

Keywords

Limit theorem Fractional Brownian motion Method of moments Short range dependence 

Mathematics Subject Classification (2010)

Primary 60F17 Secondary 60G15 60G22 

Notes

Acknowledgments

We would like to thank two anonymous referees and an associate editor for carefully reading this manuscript and making helpful remarks.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Finance and StatisticsEast China Normal UniversityShanghaiChina

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