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Biometrika 1975 62(2):497-501; doi:10.1093/biomet/62.2.497
© 1975 by Biometrika Trust
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Unique estimates of the parameters of a continuous stationary stochastic process

S. M. PANDIT and S. M. WU

Department of Machanical Engineering, University of Wisconsin Madison

Explicit parametric relations are derived between the parameters of a continuos time stationary stochastic process governed by a second-order linear differential equation and its uniformly sampled discrete representation. These relations are used to analyze and resolve the multiplicity of the parameters of the continuous process estimated from sampled data, leading to alias-free estimates of spectra. A limiting case of the sampled process, including integrated random walk, is pointed out. The estimation procedure is illustrated by data obtained from a mechanical system.

Key Words: Alias-free spectral estimate • Integrated random walk • Stochastic differential equation • Time series • Vibration system


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