Brownian Motion Indexed by a Time Scale
Ladde, G. S.
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.
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
Mathematics and Statistics
Keywords and Phrases
Brownian motion; Kolmogorov-Centsov Theorem; Stochastic dynamic equations; time scales
Article - Journal
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