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February 1999 Bilinear stochastic systems with fractional Brownian motion input
E. Iglói, Gy. Terdik
Ann. Appl. Probab. 9(1): 46-77 (February 1999). DOI: 10.1214/aoap/1029962597


The partial derivatives with respect to time and the fractional Brownian motion of a particular class of stationary processes are defined. Although the fractional Brownian motion is not semimartingale, the bilinear SDE with fractional Brownian motion input is considered and solved. The solution is explicitly given in both the frequency and time domains in the case when the coefficient of the bilinear term is pure imaginary. The stationary Stratonovich solution of the bilinear SDE with white noise input is also considered.


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E. Iglói. Gy. Terdik. "Bilinear stochastic systems with fractional Brownian motion input." Ann. Appl. Probab. 9 (1) 46 - 77, February 1999.


Published: February 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0948.60050
MathSciNet: MR1682600
Digital Object Identifier: 10.1214/aoap/1029962597

Primary: 60H05
Secondary: 62M15 , 93E03

Keywords: Bilinear systems , fractional Brownian motion integrator , long-range dependence , stationarity , Stratonovich solution

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 1 • February 1999
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