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Fractional Brownian motion is a generalised Gaussian diffusive process that is found to describe numerous stochastic phenomena in physics and biology. Here we introduce a multi-dimensional fractional Brownian motion (FBM) defined as a…

Statistical Mechanics · Physics 2013-06-14 Jae-Hyung Jeon , Aleksei V. Chechkin , Ralf Metzler

This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…

Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic process with long-ranged correlations, represents a widely applied, paradigmatic mathematical model of anomalous diffusion. We report the results of…

Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…

Statistical Mechanics · Physics 2025-09-15 Jonathan House , Rashad Bakhshizada , Skirmantas Janušonis , Ralf Metzler , Thomas Vojta

Fractional Brownian motion (fBm) is an important scale-invariant Gaussian non-Markovian process with stationary increments, which serves as a prototypical example of a system with long-range temporal correlations and anomalous diffusion.…

Statistical Mechanics · Physics 2026-04-29 Baruch Meerson , Pavel V. Sasorov

The analysis of local minima in time series data and random landscapes is essential across numerous scientific disciplines, offering critical insights into system dynamics. Recently, Kundu, Majumdar, and Schehr derived the exact…

Statistical Mechanics · Physics 2026-03-19 Maxim Dolgushev , Olivier Bénichou

Heterogeneous diffusion processes are prevalent in various fields, including the motion of proteins in living cells, the migratory movement of birds and mammals, and finance. These processes are often characterized by time-varying dynamics,…

Statistical Mechanics · Physics 2025-03-11 Michał Balcerek , Adrian Pacheco-Pozo , Agnieszka Wyłomańska , Diego Krapf

Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst…

Data Analysis, Statistics and Probability · Physics 2015-05-13 Lucas Lacasa , Bartolo Luque , Jordi Luque , Juan Carlos Nuno

Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…

Statistical Mechanics · Physics 2016-09-08 Jae-Hyung Jeon , Ralf Metzler

Cell migration often exhibits long-range temporal correlations and anomalous diffusion, even in the absence of external guidance cues such as chemical gradients or topographical constraints. These observations raise a fundamental question:…

Quantitative Methods · Quantitative Biology 2025-11-25 Gustavo Cornejo-Olea , Lucas Buvinic , Jerome Darbon , Radek Erban , Andrea Ravasio , Anastasios Matzavinos

We report in this paper a thorough study on the the dynamical mechanics of the fractional Brownian motion systems. Where several non-trivial properties are revealed such as the abundant non-Markovian effects resulted from the fractional…

Statistical Mechanics · Physics 2015-02-24 Chun-Yang Wang , Shu-Qin Lv , Ming Yi

Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, which can change the structure of the underlying…

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter $H \in (0, 1)$ called the Hurst index. The use of time-changed processes in modeling often requires the…

Probability · Mathematics 2014-08-21 Jebessa B. Mijena

Fractional Brownian motion (fBm) is an experimentally-relevant, non-Markovian Gaussian stochastic process with long-ranged correlations between the increments, parametrised by the so-called Hurst exponent $H$; depending on its value the…

Statistical Mechanics · Physics 2023-10-04 O. Benichou , G. Oshanin

Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…

Statistical Mechanics · Physics 2024-07-02 Adrian Pacheco-Pozo , Diego Krapf

The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external…

Statistical Mechanics · Physics 2023-08-31 Yingjie Liang , Wei Wang , Ralf Metzler

Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale…

Methodology · Statistics 2017-09-13 J. M. Lilly , A. M. Sykulski , J. J Early , S. C. Olhede

Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…

Statistical Mechanics · Physics 2019-03-22 T. Guggenberger , G. Pagnini , T. Vojta , R. Metzler

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC)…

Computation · Statistics 2022-11-02 Mohamed Maama , Ajay Jasra , Hernando Ombao

Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic…

Probability · Mathematics 2013-05-03 Joachim Lebovits
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