Archivio Istituzionale della RicercaWe transform an initial value problem for a stochastic differential equation to the time-frequency domain. The result is a deterministic time-frequency equation whose forcing term incorporates the given set of initial values. The structure and solution of the time-frequency equation reveal the spectral properties of the nonstationary random process solution to the stochastic differential equation. By applying our method to the Langevin equation, we obtain the exact time-frequency spectrum for an arbitrary initial value.
Initial Value Problems in the Time-Frequency Domain / Galleani, Lorenzo - In: Pseudo-Differential Operators, Generalized Functions and Asymptotics / Molahajloo S., Pilipović S., Toft J., Wong M. W.. - STAMPA. - Basel : Birkhauser -- Springer Basel, 2013. - ISBN 9783034808033. - pp. 189-197 [10.1007/978-3-0348-0585-8_9]
Initial Value Problems in the Time-Frequency Domain
GALLEANI, Lorenzo
2013
Abstract
We transform an initial value problem for a stochastic differential equation to the time-frequency domain. The result is a deterministic time-frequency equation whose forcing term incorporates the given set of initial values. The structure and solution of the time-frequency equation reveal the spectral properties of the nonstationary random process solution to the stochastic differential equation. By applying our method to the Langevin equation, we obtain the exact time-frequency spectrum for an arbitrary initial value.
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https://hdl.handle.net/11583/2500847
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