Title

Brownian Motion Indexed by a Time Scale

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

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

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2011 Taylor & Francis, All rights reserved.

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