Brownian Motion Indexed by a Time Scale

Author

David E. Grow, Missouri University of Science and TechnologyFollow
Suman Sanyal

Editor(s)

Ladde, G. S.

Abstract

In this article, we generalize Wiener's existence result for one-dimensional Brownian motion by constructing a suitable continuous stochastic process where the index set is a time scale. We construct a countable dense subset of a time scale and use it to prove a generalized version of the Kolmogorov-Čentsov theorem. As a corollary, we obtain a local Hölder-continuity result for the sample paths of generalized Brownian motion indexed by a time scale.

Recommended Citation

D. E. Grow and S. Sanyal, "Brownian Motion Indexed by a Time Scale," Stochastic Analysis and Applications, Taylor & Francis, Jan 2011.

The definitive version is available at https://doi.org/10.1080/07362994.2011.564441

Department(s)

Mathematics and Statistics

Keywords and Phrases

Brownian motion; Kolmogorov-Centsov Theorem; Stochastic dynamic equations; time scales

International Standard Serial Number (ISSN)

0736-2994

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2011 Taylor & Francis, All rights reserved.

Publication Date

01 Jan 2011