![](images/spacer.gif) |
|
|
| | | | | |
|
|
|
|
|
A remark on the equivalence of Gaussian processes
|
Harry van Zanten, Vrije Universiteit Amsterdam |
Abstract
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.
|
Full text: PDF
Pages: 54-59
Published on: February 4, 2008
|
Bibliography
-
Baudoin, F. and Nualart, D. (2003).
Equivalence of Volterra processes.
Stochastic Process. Appl. 107(2), 327-350.
MR1999794
-
Cheridito, P. (2001).
Mixed fractional Brownian motion.
Bernoulli 7(6), 913-934.
MR1873835
-
Doob, J.L. (1953).
Stochastic processes.
John Wiley & Sons Inc., New York.
MR0058896
-
Dym, H. and McKean, H.P. (1976).
Gaussian processes, function theory, and the inverse spectral
problem.
Academic Press, New York.
MR0448523
-
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.
MR2123205
-
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.
MR2178502
-
Gihman, I.I. and Skorohod, A.V. (1980).
The theory of stochastic processes I.
Springer-Verlag, Berlin.
MR0636254
-
Ibragimov, I.A. and Rozanov, Y.A. (1978).
Gaussian random processes.
Springer-Verlag, New York.
MR0543837
-
Samorodnitsky, G. and Taqqu, M.S. (1994).
Stable non-Gaussian random processes.
Chapman & Hall, New York.
MR1280932
-
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.
MR2287103
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|