Besov Orlicz Spaces Research Articles

Best Spline Approximation in Besov-Orlicz Space

Orlicz spaces have got the attention of many researchers over the decades. Many spaces have been defined in terms of Orlicz spaces, in particular Besov-Orlicz spaces. In this paper, we discuss this class of spaces with modulus of continuity. We study the best approximation of Besov-Orlicz spaces with splines and polynomials. The degree of best approximation depends on modulus of continuity.

Path Regularity of the Brownian Motion and the Brownian Sheet

By the work of P. Lévy, the sample paths of the Brownian motion are known to satisfy a certain Hölder regularity condition almost surely. This was later improved by Ciesielski, who studied the regularity of these paths in Besov and Besov-Orlicz spaces. We review these results and propose new function spaces of Besov type, strictly smaller than those of Ciesielski and Lévy, in which the sample paths of the Brownian motion almost surely lie. In the same spirit, we review and extend the work of Kamont, who investigated the same question for the multivariate Brownian sheet and function spaces of dominating mixed smoothness.

On the embedding of BV space into Besov-Orlicz space

We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces to be bounded. The condition has a form of a simple integral inequality involving Young and weight functions. We provide an example with Matuszewska-Orlicz indices of involved Orlicz norm equal to one. The main tool is the molecular decomposition of functions from a BV space.

On temporal regularity of stochastic convolutions in $2$-smooth Banach spaces

Nous montrons que les trajectoires des solutions des equations aux derivees partielles stochastiques paraboliques ont la meme regularite en temps que le processus de Wiener (aussi loin que vont les connaissances actuelles en la matiere). La regularite temporelle est consideree dans l’espace de Besov–Orlicz $B^{1/2}_{\Phi _{2},\infty }(0,T;X)$ ou $\Phi _{2}(x)=\exp (x^{2})-1$ et $X$ est un espace de Banach $2$-lisse.

Stroock-Varadhan support theorem for random evolution equation in Besov-Orlicz spaces

We consider the family of stochastic processes $X=\{X_t, t\in [0;1]\}\,,$ where $X$ is the solution of the It\^{o} stochastic differential equation \[dX_t = \sigma(X_t, Z_t)dW_t + b(X_t,Y_t) dt \hspace*{2cm}\] whose coefficients Lipschitzian depend on $Z=\{Z_t, t\in [0;1]\} $ and $Y=\{Y_t, t\in [0;1]\}$. We prove that the trajectories of $X$ a.s. belong to the Besov-Orlicz space defined by the f nction $M(x)=e^{x^2}-1$ and the modulus of continuity $\omega(t)=\sqrt{t\log(1/t)}$. The aim of this work is to characterize the support of the law $X$ in this space.

Support of solutions of stochastic differential equations in exponential Besov–Orlicz spaces

The Besov–Orlicz space with is currently the smallest known classical function space to which paths of the Wiener process belong almost surely. We consider stochastic differential equations with no global growth condition on the non-linearities and we describe the topological support of the laws of trajectories of the solutions in every Polish subspace of continuous functions into which the Besov–Orlicz space is embedded compactly.

Weak convergence in a class of anisotropic Besov–Orlicz space

AbstractThe main result of this paper is a new tightness criterion in a class of anisotropic Besov–Orlicz spaces. This result generalizes those obtained by Boufoussi and Lakhel [

Tightness in Besov–Orlicz spaces: Characterizations and applications

AbstractWe establish a tightness criterion in a class of Besov–Orlicz spaces. Our result generalizes those obtained in [

LIMIT THEOREMS FOR A CLASS OF ADDITIVE FUNCTIONALS OF SYMMETRIC STABLE PROCESS AND FRACTIONAL BROWNIAN MOTION IN BESOV-ORLICZ SPACES

We use the Potter’s Theorem and the tightness criterion in Besov-Orlicz spaces, recently proved, to generalize some limit theorem for occupation times problem of certain self-similar process, namely symmetric stable process of index 1<α≤ and fractional Brownian motion of Hurst parameter 0

Remarks on the critical Besov space and its embedding into weighted Besov–Orlicz spaces

We present several continuous embeddings of the critical Besov space $B^{{n}/{p},\rho}_p(\Bbb R^n)$. We first establish a Gagliardo-Nirenberg type estimate $$ \|u\|_{\dot B^{0,\nu}_{q,w_r}}\leq C_n\left(\frac{1}{n-r}\right)^{\frac{1}{q}+\frac{1}{\nu}-\fra

Lions-Peetre's Interpolation Methods Associated with Quasi-Power Functions and Some Applications

This paper concerns some properties of Lions-Peetre's interpolation methods of constants and means associated with quasi-power functions, and their applications in harmonic analysis, martingale inequalities, and geometric properties of Banach spaces. We describe Besov-Orlicz spaces and Triebel-Lizorkin-Orlicz spaces in terms of interpolation and wavelet bases. We study the commutators of quasi-logarithmic operators and singular integral operators, Hankel operators in Schatten-Orlicz classes, martingale inequalities for the partial derivative-variation, and the stability of multi-dimensional uniform rotundity under interpolation.

Large deviation for stochastic volterra equation in the Besov-Orlicz space and application

Large deviation for stochastic volterra equation in the Besov-Orlicz space and application

Large deviation for stochastic volterra equation in the Besov-Orlicz space and application

Large deviation for stochastic volterra equation in the Besov-Orlicz space and application

Freidliln–Wentzell type estimates for solutions of hyperbolic SPDEs in Besov–Orlicz spaces and applications

In this paper,we firstly study the regularity of solutions of hyperbolic stochastic partial differential equations by proving that they almost surely belong to the anisotropic Besov–Orlicz space corresponding to the Young function M2(t)= exp (t 2) - 1. Secondly, we establish a large deviation principle in this space for the law of the solutions which generalizes the result in Eddahbi [16] dealing with the Höder topology, weaker than the Besov-Orlicz topology the Strassen's iterated logarithm law for the Brownian sheet obtained in N’zi [29].

Large deviations for a stochastic Volterra-type equation in the Besov–Orlicz space

In this paper, we investigate the regularity of the solutions of a class of two-parameter Stochastic Volterra-type equations in the anisotropic Besov–Orlicz space B τ,ω 0 modulated by the Young function τ( t)=exp( t 2)−1 and the modulus of continuity ω( t)=( t(1+log(1/ t))) 1/2. Moreover, we derive in the Besov–Orlicz norm a large deviation estimate of Freidlin–Wentzell type for the solution.

Régularité Besov-Orlicz du temps local brownien

Let (B t, t ε [ 0, 1]) be a linear Brownian motion starting from 0 and denote (L t(x), t ≥ 0, x ∈ ℝ) its local time. We prove that, for all t > 0, a.s. the function xL t (x) belongs to the Besov-Orlicz space B ½ M 2, ∞ with M 2( x)= e |x| 2 -1 and doesn't belong a.s. to B ½,0 M 2, ∞.