Stochastic Modelling of Deterministic Time Series

The proposed research project will implement and further develop the methods of Stemler et al. for modelling deterministic time series with stochastic models. The project will implement the Kramers-Moyal expansion to determine Fokker-Planck coefficients of a deterministic time series. Furthermore, these methods will be applied to gain new insights into a chaotic semiconductor laser driven by optical feedback, whose noise appears dynamical and state dependent. The major research components of the proposed project are developing appropriate stochastic models for deterministic time series and adapting these methods to better understand the noise component of a chaotic semiconductor laser driven by optical feedback.

Jack Mulqueeney

The University of Western Australia

Jack is a third year student at the University of Western Australia studying mathematics, statistics, and economics. He is interested in the application of mathematics to understand various types of behaviour, both physical and social. For this reason, he conducted a research project on mathematical and stochastic properties of networks in his second year. Furthermore, he completed an internship at a Perth NFP, Communicare, which ignited his interest in social behaviour and how mathematics can be applied to such systems. His research interests lie in modelling behaviour accurately to gain insights into their fundamental properties and forecasting, with some degree of confidence, their behaviour into the future.

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