On the wavelet-based simulation of anomalous diffusion

Gustavo Didier, John Fricks

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The field of microrheology is based on experiments involving particle diffusion. Microscopic tracer beads are placed into a non-Newtonian fluid and tracked using high speed video capture and light microscopy. The modelling of the behaviour of these beads is now an active scientific area which demands multiple stochastic and statistical methods. We propose an approximate wavelet-based simulation technique for two classes of continuous time anomalous diffusion models, the fractional Ornstein-Uhlenbeck process and the fractional generalized Langevin equation. The proposed algorithm is an iterative method that provides approximate discretizations that converge quickly and in an appropriate sense to the continuous time target process. As compared to previous works, it covers cases where the natural discretization of the target process does not have closed form in the time domain. Moreover, we propose to minimize the border effect via smoothing.

Original languageEnglish (US)
Pages (from-to)697-723
Number of pages27
JournalJournal of Statistical Computation and Simulation
Volume84
Issue number4
DOIs
StatePublished - 2014
Externally publishedYes

Fingerprint

Anomalous Diffusion
Continuous Time
Wavelets
Fractional
Discretization
Generalized Langevin Equation
Smoothing Effect
Target
Ornstein-Uhlenbeck Process
Non-Newtonian Fluid
Stochastic Methods
Diffusion Model
Iterative methods
Microscopy
Statistical method
Optical microscopy
Time Domain
Statistical methods
Simulation
Closed-form

Keywords

  • anomalous diffusion
  • fractional Ornstein-Uhlenbeck process
  • generalized Langevin equation
  • simulation
  • wavelets

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty

Cite this

On the wavelet-based simulation of anomalous diffusion. / Didier, Gustavo; Fricks, John.

In: Journal of Statistical Computation and Simulation, Vol. 84, No. 4, 2014, p. 697-723.

Research output: Contribution to journalArticle

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