Related papers: Fractional Brownian motion in a nutshell
As an extension of isotropic Gaussian random fields and Q-Wiener processes on d-dimensional spheres, isotropic Q-fractional Brownian motion is introduced and sample H\"older regularity in space-time is shown depending on the regularity of…
The main goal of this paper is to provide a fractional stochastic differential equation modelling the physical phenomena governed by the Langevin equation in 1-dimension. A generalized equation leaning on the fractional Brownian motion…
Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations <x(t)x(s)> ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with 0<H<1 is called the Hurst exponent. For H = 1/2, x(t) is a Brownian motion, while for H…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
A time-changed fractional mixed fractional Brownian motion by inverse alpha stable subordinator with index alpha in (0, 1) is an iterated process L constructed as the superposition of fractional mixed fractional Brownian motion N(a, b) and…
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the…
A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures $M[0,t], 0\le t\le1$. In this paper we obtain an extension of this process, referred to as multifractal…
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…
We show that if a random variable is the final value of an adapted log-H\"{o}lder continuous process, then it can be represented as a stochastic integral with respect to a fractional Brownian motion with adapted integrand. In order to…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the…
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…
Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst…
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…
The fractional Brownian motion is a generalization of ordinary Brownian motion, used particularly when long-range dependence is required. Its explicit introduction is due to B.B. Mandelbrot and J.W. van Ness (1968) as a self-similar…
We represent fractional conditional expectations of a functional of fractional Brownian motion as a convergent series in L^2 space. When the target random variable is some function of a discrete trajectory of fractional Brownian motion, we…
This is a pedagogical introduction to Brownian motion on the occasion of the 100th anniversary of Einstein's 1905 paper on the subject. After briefly reviewing Einstein's work in its contemporary context, we pursue some lines of further…
Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the…
Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of…
A well-known result with respect to the one dimensional nearest-neighbor symmetric simple exclusion process is the convergence to fractional Brownian motion with Hurst parameter 1/4, in the sense of finite-dimensional distributions, of the…