Daniel completed a BSc at La Trobe University, Melbourne, with majors in mathematics and statistics. He will study Honours in 2017 with a focus on probability theory and statistics, though he will also take subjects in topology, general (universal) algebra and computation. His academic interests also include programming, optimisation, data structures, machine learning, semantic web technology, economics and education. Outside of his studies Daniel is an enthusiastic cat owner, an infrequent scuba diver, and a volunteer with the Victorian SES.
Daniel helped found the La Trobe University Mathematics and Statistics Society (LUMSS), where in the future he hopes to work on increasing the appeal and accessibility of science education for all. As a late learner of mathematics (starting off in humanities) he is inspired to help others see the light. He was honoured to receive the Professor C.J. Eliezer prize in second year mathematics, as well as the Professor Jim Morrison Prize in first year chemistry.
Functionals of long-range dependent fields and Hermite distributions
The project will investigate asymptotic properties of functionals of long range dependent random fields and processes. Distributions of multiple Wiener-Itô stochastic integrals in non-central limit theorems will be studied. For functionals of Hermite rank κ distributional properties of their asymptotics are almost unknown. Novel random series representations of these asymptotics will be used as the main tool. Visualisation and simulation studies of the asymptotic distributions will be performed using R and Maple software.