Related papers: Regularity of Weighted Tensorized Fractional Brown…

This paper presents a new model of textures, obtained as realizations of a new class of fractional Brownian fields. These fields, called weighted tensorized fractional Brownian fields, are obtained by a relaxation of the tensor-product…

In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are…

We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values…

We explore a generalisation of the L\'evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all…

We illustrate the cosmological Friedmann-Robertson-Walker (FRW) models realized as gauge theory in the extended configuration space with its Becchi-Rouet-Stora-Tyutin (BRST) invariance upto total derivative. To investigate the model in…

Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space $VB_{p,q}^{\delta,w}(\mathbb{R}^d)$ whose…

We construct absolute continuous stochastic processes that converge to anisotropic fractional and multifractional Brownian sheets in Besov-type spaces.

This paper studies the following weighted, fractional Bernstein inequality for spherical polynomials on $\sph$: \begin{equation}\label{4-1-TD-ab} \|(-\Delta_0)^{r/2} f\|_{p,w}\leq C_w n^{r} \|f\|_{p,w}, \ \ \forall f\in \Pi_n^d,…

Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ satisfying Gaussian upper bounds on its heat kernels. In this paper we develop the theory of weighted Besov spaces…

The present article is concerned with the nonlinear approximation of functions in the Sobolev space H^q with respect to a tensor-product, or hyperbolic wavelet basis on the unit n-cube. Here, q is a real number, which is not necessarily…

We describe two classes of Gaussian self-similar random fields: with strictly stationary rectangular increments and with mild stationary rectangular increments. We find explicit spectral and moving average representations for the fields…

We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized function spaces. We obtain precise…

We develop a statistical field theory that describes the large-N limit of a system of Brownian particles with quenched random pairwise interactions on a compact two-dimensional Riemannian manifold. The resulting Frustrated Fields (F2) model…

We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under…

We discuss a family of random fields indexed by a parameter $s\in \mathbb{R}$ which we call the fractional Gaussian fields, given by \[ \mathrm{FGF}_s(\mathbb{R}^d)=(-\Delta)^{-s/2} W, \] where $W$ is a white noise on $\mathbb{R}^d$ and…

We here construct (large) local and small global-in-time regular unique solutions to the fractional Euler alignment system in the whole space ${\mathbb R}^d$, in the case where the deviation of the initial density from a constant is…

Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…

Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show…

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…

Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of…