Rogans, Michael2019-10-032019-10-032018https://hdl.handle.net/10539/28195It is being submitted for the Degree of Doctor of Philosophy in the University of the Witwatersrand, Johannesburg. Signed on the 29th day of November 2018, at Johannesburg, South Africa.Various contributions have been made to the study of stochastic processes in the abstract setting of Riesz spaces, and include topics such as conditional expectation, martingales and independence. This dissertation provides a review of those topics and extends the work done by Grobler, Kuo, Labuschagne, Stoica, Watson and others by considering the notions of mixing, mixingales and near-epoch dependence in a Riesz space.enThesis