Related papers: Fractional Normal Inverse Gaussian Process
In this paper we present a general mathematical construction that allows us to define a parametric class of $H$-sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some…
The Wiener's path integral plays a central role in the studies of Brownian motion. Here we derive exact path-integral representations for the more general \emph{fractional} Brownian motion (fBm) and for its time derivative process -- the…
We consider the paths of a Gaussian random process $x(t)$, $x(0)=0$ not exceeding a fixed positive level over a large time interval $(0,T)$, $T\gg 1$. The probability $p(T)$ of such event is frequently a regularly varying function at…
In this paper, we unify popular non-rigid registration methods for point sets and surfaces under our general framework, GiNGR. GiNGR builds upon Gaussian Process Morphable Models (GPMM) and hence separates modeling the deformation prior…
The Lamperti transform offers a powerful bridge between self-similar processes and stationary dynamics, making it especially useful for analyzing anomalous diffusion models that lack stationary increments. In this paper we examine the…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
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…
Fractional Brownian motion, H-FBM , of index 0<H<1 is considered as initial velocity in the inviscid Burgers equation. It is shown that the Hausdorff dimension of regular Lagrangian points at any moment t is equal to H. This fact validates…
Sub-fractional Brownian motion is a process analogous to fractional Brownian motion but without stationary increments. In \cite{GGL1} we proved a strong uniform approximation with a rate of convergence for fractional Brownian motion by…
In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion $B^{H,K}$ with parameters $H\in (0,1)$ and $K\in(1,2)$ such that $HK\in(0,1)$. A remarkable difference between the case…
Bifractional Brownian motion on $\mathbb{R}_+$ is a two parameter centered Gaussian process with covariance function: \[ R_{H,K} (t,s)=\frac 1{2^K}\left(\left(t^{2H}+s^{2H}\right)^K-\ |{t-s}\ |^{2HK}\right), \qquad s,t\ge 0. \] This process…
We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an…
We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ and multiplicative noise component $\sigma$. When…
This paper studies the first hitting times of generalized Poisson processes $N^f(t)$, related to Bernstein functions $f$. For the space-fractional Poisson processes, $N^\alpha(t)$, $t>0$ (corresponding to $f= x^\alpha$), the hitting…
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…
We investigate a special case of infinite urn schemes first considered by Karlin (1967), especially its occupancy and odd-occupancy processes. We first propose a natural randomization of these two processes and their decompositions. We then…
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We…
In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…