Related papers: Weighted tensorized fractional Brownian textures
In this paper, we define a new and broad family of vector-valued random fields called tempered operator fractional operator-stable random fields (TRF, for short). TRF is typically non-Gaussian and generalizes tempered fractional stable…
This paper is concerned with the backward stochastic differential equations whose generator is a weighted fractional Brownian field: $Y_t=\xi+\int_t^T Y_s W (ds,B_s) -\int_t^T Z_sdB_s$, $0\le t\le T$, where $W$ is a $(d+1)$-parameter…
We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of…
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…
Security of oscillatory true random number generators remains not fully understood due to insufficient understanding of complex $1/f^\alpha$ phase noise. To bridge this gap, we introduce fractional Brownian motion as a comprehensive…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
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…
In the paper we investigate statistical and topological properties of fractional Brownian polymer chains, equipped with the short-range volume interactions. The attention is paid to statistical properties of collapsed conformations with the…
One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relying on geometric ideas reminiscent of the…
This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its covariance operator, asymptotically accurate up to the…
We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded…
In recent years, substantial progress has been achieved in learning-based reconstruction of 3D objects. At the same time, generative models were proposed that can generate highly realistic images. However, despite this success in these…
Stochastic transport due to a velocity field modeled by the superposition of small-scale divergence free vector fields activated by Fractional Gaussian Noises (FGN) is numerically investigated. We present two non-trivial contributions: the…
We propose discrete random-field models that are based on random partitions of $\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established…
The measurement of shear stress acting on a biologically relevant surface is a challenging problem, particularly in the complex environment of, for example, the vasculature. While an experimental method for the direct detection of wall…
Here we introduce a new model of natural textures based on the feature spaces of convolutional neural networks optimised for object recognition. Samples from the model are of high perceptual quality demonstrating the generative power of…
In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to…
This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and…