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

Henryk Gzyl ()

Statistics & Probability Letters, 2021, vol. 179, issue C

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.

Keywords: Gauss–Markov process; Wave equation; Harmonic oscillator; Cameron–Martin-Girsanov–Maruyama change of measure (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715221001942
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:179:y:2021:i:c:s0167715221001942

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2021.109232

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().