Constructing stationary Gaussian processes from deterministic processes with random initial conditions

Loading...
Thumbnail Image

View/Download File

Persistent link to this item

Statistics
View Statistics

Journal Title

Journal ISSN

Volume Title

Title

Constructing stationary Gaussian processes from deterministic processes with random initial conditions

Alternative title

Published Date

2002-06

Publisher

Type

Abstract

We consider a family of stationary Gaussian processes that includes the stationary Ornstein-Uhlenbeck process. We show that processes in this family can be attained as the limit of a sequence of deterministic processes with random initial conditions. Weak convergence in the supremum norm on finite time-intervals is shown. We also establish the convergence of a wide variety of long-term statistics. Our construction provides a rigorous example of how macroscopic stochastic dynamics can be derived from microscopic deterministic dynamics.

Keywords

Description

Replaces

License

Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Other identifiers

Suggested citation

Tupper, P.F.. (2002). Constructing stationary Gaussian processes from deterministic processes with random initial conditions. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3776.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.