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Forced harmonic oscillators, waves on a forced string and changes of measure

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  • Gzyl, Henryk

Abstract

There is a connection between deterministic Gaussian processes, that is, flows that leave a Gaussian measure invariant and waves on a string. The connection appears when the solution to the wave equation is expanded in the eigenvalues of the Laplacian. The Fourier components behave as one dimensional harmonic oscillators. It so happens that if the initial conditions of each deterministic oscillator have an appropriate Gaussian distribution, then the motion of the oscillator in its phase space leaves it invariant.

Suggested Citation

  • Gzyl, Henryk, 2021. "Forced harmonic oscillators, waves on a forced string and changes of measure," Statistics & Probability Letters, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:stapro:v:179:y:2021:i:c:s0167715221001942
    DOI: 10.1016/j.spl.2021.109232
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    References listed on IDEAS

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    1. Gzyl, Henryk, 1987. "Characterization of vector valued, gaussian, stationary, markov processes," Statistics & Probability Letters, Elsevier, vol. 6(1), pages 17-19, September.
    2. Gzyl, Henryk, 2021. "Harmonic oscillators, waves and Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 172(C).
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    1. Gzyl, Henryk, 2021. "Harmonic oscillators, waves and Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 172(C).

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