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ANOMALOUS DIFFUSION PROCESSES: STOCHASTIC MODELS AND THEIR PROPERTIES

Part of: Stochastic processes Inference from stochastic processes Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  27 March 2020

SEAN CARNAFFAN
SEAN CARNAFFAN*
Affiliation:
School of Mathematics and Statistics,University of Sydney, Camperdown, NSW2006, Australia email scarnaffan@gmail.com
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Abstract

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Keywords

anomalous diffusionstochastic processes

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 35Q84: Fokker-Planck equations 62M09: Non-Markovian processes
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 514 - 517
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to the University of Sydney in July 2019; degree approved on 1 October 2019; supervisor Reiichiro Kawai.

References

Carnaffan, S. and Kawai, R., ‘Cusping, transport and variance of solutions to generalized Fokker–Planck equations’, J. Phys. A 50(24) (2017), Article ID 245001.CrossRefGoogle Scholar
Carnaffan, S. and Kawai, R., ‘Solving multidimensional fractional Fokker–Planck equations via unbiased density formulas for anomalous diffusion processes’, SIAM J. Sci. Comput. 39(5) (2017), B886–B915.10.1137/17M111482XCrossRefGoogle Scholar
Carnaffan, S. and Kawai, R., ‘Analytic model for transient anomalous diffusion with highly persistent correlations’, Phys. Rev. E 99(6) (2019), Article ID 062120.10.1103/PhysRevE.99.062120CrossRefGoogle ScholarPubMed
Carnaffan, S. and Kawai, R., ‘Optimal statistical inference for subdiffusion processes’, J. Phys. A 52(13) (2019), Article ID 135001.10.1088/1751-8121/ab0769CrossRefGoogle Scholar