Master of Science - Research
School of Mathematics and Applied Statistics
Ismael, Mimoon Ibrahim, Recurrence times in stochastic processes and dynamical systems, Master of Science - Research thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2013. https://ro.uow.edu.au/theses/3997
In this work we consider various aspects of recurrence times in stochastic processes and dynamical systems. The first part of the thesis is set in the context of zero-one stochastic processes. Here, by a zero-one stochastic pro- cess is meant a sequence of functions on a given set where each function takes values of either zero or one. The discussion is primarily concerned with stationary processes and is a rigourous and, in some aspects, a more general discussion of work of P. Kasteleyn. A connection between notions of recurrence in zero-one stochastic processes and dynamical systems admitting an invariant probability is established. The later part of the thesis presents new results in some special dynamical systems. These results are mainly to do with calculating the standard deviation of recurrence times and discussing the fininteness of the standard deviation, and are related to the existing literature.
Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.