Electronic Communications in Probability

A remark on the equivalence of Gaussian processes

Harry van Zanten

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In this note we extend a classical equivalence result for Gaussian stationary processes to the more general setting of Gaussian processes with stationary increments. This will allow us to apply it in the setting of aggregated independent fractional Brownian motions.

Article information

Electron. Commun. Probab., Volume 13 (2008), paper no. 6, 54-59.

Accepted: 4 February 2008
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes
Secondary: 60G30: Continuity and singularity of induced measures

Gaussian processes with stationary increments equivalence of laws spectral method

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van Zanten, Harry. A remark on the equivalence of Gaussian processes. Electron. Commun. Probab. 13 (2008), paper no. 6, 54--59. doi:10.1214/ECP.v13-1348. https://projecteuclid.org/euclid.ecp/1465233433

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  • Baudoin, F. and Nualart, D. (2003). Equivalence of Volterra processes. Stochastic Process. Appl. 107(2), 327-350.
  • Cheridito, P. (2001). Mixed fractional Brownian motion. Bernoulli 7(6), 913-934.
  • Doob, J.L. (1953). Stochastic processes. John Wiley & Sons Inc., New York.
  • Dym, H. and McKean, H.P. (1976). Gaussian processes, function theory, and the inverse spectral problem. Academic Press, New York.
  • Dzhaparidze, K. and Van Zanten, J.H. (2005). Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion. Ann. Probab. 33(2), 620-644.
  • Dzhaparidze, K., Van Zanten, J.H. and Zareba, P. (2005). Representations of fractional Brownian motion using vibrating strings. Stochastic Process. Appl. 115(12), 1928-1953.
  • Gihman, I.I. and Skorohod, A.V. (1980). The theory of stochastic processes I. Springer-Verlag, Berlin.
  • Ibragimov, I.A. and Rozanov, Y.A. (1978). Gaussian random processes. Springer-Verlag, New York.
  • Samorodnitsky, G. and Taqqu, M.S. (1994). Stable non-Gaussian random processes. Chapman & Hall, New York.
  • Van Zanten, J.H. (2007). When is a linear combination of independent fBm's equivalent to a single fBm? Stochastic Process. Appl. 117(1), 57-70.