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

• Published in: Statistics & probability letters Vol. 179; p. 109232
• Main Author: Gzyl, Henryk
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2021
• Subjects: Cameron–Martin-Girsanov–Maruyama change of measure; Gauss–Markov process; Harmonic oscillator; Wave equation; Wave equation; Gauss–Markov process; Cameron–Martin-Girsanov–Maruyama change of measure; Harmonic oscillator

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 dimensiona...