Fractional Brownian Motions

By Hai Le. Acta Physica Polonica B, 2020

188 citations recorded by the source corpus.

1 The project The term Fractional Brownian motions (fBm’s) were first used by Mandelbrot and van Ness in their seminal paper “Fractional Brownian motions, fractional noises and applications” to give a generalization to the standard Brownian motions. They realized fBm’s sometimes serve as a better model for many random phenomena because of its “interdependence between distant samples”. What that means informally is the change in the future will depend on the changes in the past, unlike in the case of standard Brownian motions where the changes are independent of each other. Consequently, fBm’s have found applications in modeling random processes appearing in economics, finance, hydrology, wave propagation in random media, etc.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/2d930848a333c208978f33d2b8c8c156dd791b65

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In Economics and Econometrics

Khoa Le

In Finance

Citations in the corpus

Rough Volatility: Fact or Artefact? (2022, unknown): “dence to ‘rough volatility’ Beginning with Mandelbrot and VanNess [22], fractional Brownian motion and fractional Gaussian noise have been used as building blocks of stochastic models of various phenomena in physics, engineering [21] and finance [2, 5, 7, 9, 16, 26, 28].”
A stochastic sewing lemma and applications (2018, background): “The fractional Brownian motion BH admits a moving average representation which was introduced by Mandelbrot and Van Ness [33] BHt = C(H) ∫ t −∞ [(t− r)H− 1 2 + − (−r)H− 1 2 ]dW̃r for every t ≥ 0, where C(H) is a suitable normalizing constant and W̃ is a two-sided Brownian motion.”
Semilinear Caputo time-fractional pseudo-parabolic equations (2021, background): “Many important physical models and practical problems require us to consider the pseudo-parabolic model with fractional derivative rather than classical one, like the physical model considering memory effects [18, 19, 13, 48] and some corresponding engineering problems [4, 5, 7, 44, 46, 50, 56], esp”