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Assouad Dimension of Random Processes

Part of: Markov processes Classical measure theory Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  16 November 2018

Douglas C. Howroyd  and
Han Yu
Douglas C. Howroyd*
Affiliation:
School of Mathematics & Statistics, University of St Andrews, St Andrews KY16 9SS, UK (dch8@st-andrews.ac.uk; hy25@st-andrews.ac.uk)
Han Yu
Affiliation:
School of Mathematics & Statistics, University of St Andrews, St Andrews KY16 9SS, UK (dch8@st-andrews.ac.uk; hy25@st-andrews.ac.uk)
*
*Corresponding author.
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Abstract

In this paper we study the Assouad dimension of graphs of certain Lévy processes and functions defined by stochastic integrals. We do this by introducing a convenient condition which guarantees a graph to have full Assouad dimension and then show that graphs of our studied processes satisfy this condition.

Keywords

Brownian motionWiener processstochastic integralAssouad dimensiongraph

MSC classification

Primary: 28A80: Fractals
Secondary: 60J65: Brownian motion 60G22: Fractional processes, including fractional Brownian motion 60H05: Stochastic integrals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 281 - 290
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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