Related papers: Multifractal analysis of L\'evy fields
Kuznetsov et al. (2011) and Kuznetsov and Pardo (2013) introduced the family of Hypergeometric L\'evy processes. They appear naturally in the study of fluctuations of stable processes when one analyses stable processes through the theory of…
We use sequences which depend on two parameters to define families of ultradifferentiable functions which contain Gevrey classes. It is shown that such families are closed under superposition, and therefore inverse closed as well.…
We recall first the relations between the syzygies of the Jacobian ideal of the defining equation for a projective hypersurface $V$ with isolated singularities and the versality properties of $V$, as studied by du Plessis and Wall. Then we…
We study the composition of bivariate L\'evy process with bivariate inverse subordinator. The explicit expressions for its dispersion and auto correlation matrices are obtained. Also, the time-changed two parameter L\'evy processes with…
To model subsurface flow in uncertain heterogeneous\ fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient - also called random field - may be used. In case of a one-dimensional parameter space, L\'evy…
The multimomentum Hamiltonian formalism is applied to field systems represented by sections of composite manifolds $Y\to\Si\to X$ where sections of $\Si\to X$ are parameter fields, e.g., Higgs fields and gravitational fields. Their values…
Initiated by Polyakov in his 1981 seminal work, the study of two-dimensional Liouville Conformal Field Theory has drawn considerable attention over the past decades. Recent progress in the understanding of conformal geometry in dimension…
A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known L\'evy area, in particular the presence of an intrinsic drift of this area. Using renormalization limit of Markov chains on…
Given a low frequency sample of an infinitely divisible moving average random field $\{\int_{\mathbb{R}^d} f(x-t)\Lambda(dx); \ t \in \mathbb{R}^d \}$ with a known simple function $f$, we study the problem of nonparametric estimation of the…
We investigate the sample path regularity of multivariate operator-self-similar stable random fields with values in $\mathbb{R}^m$ given by a harmonizable representation. Such fields were introduced in [25] as a generalization of both…
In this paper, we study the multifractal analysis for Markov-R\'{e}nyi maps, which form a canonical class of piecewise differentiable interval maps, with countably many branches and may contain a parabolic fixed point simultaneously, and do…
We are concerned with a Liouville-type equation with exponential nonlinearities on a compact surface which describes the mean field equation of the equilibrium turbulence with arbitrarily signed vortices. We provide the first multiplicity…
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
We introduce L\'evy-driven causal CARMA random fields on $\mathbb{R}^d$, extending the class of CARMA processes. The definition is based on a system of stochastic partial differential equations which generalize the classical state-space…
A distributional equation as a criterion for invariant measures of Markov processes associated to L\'evy-type operators is established. This is obtained via a characterization of infinitesimally invariant measures of the associated…
In this paper our first goal is to give precise definition of the L\'evy bridges with random length. Our second task is to establish the Markov property of this process with respect to its completed natural filtration and thus with respect…
We consider an infinitely divisible random field indexed by $\mathbb{R}^d$, $d\in\mathbb{N}$, given as an integral of a kernel function with respect to a L\'evy basis with a L\'evy measure having a regularly varying right tail. First we…
We show that the general L\'{e}vy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group, ${\bf R}$. The formula of de Finetti corresponds to coboundaries. Kolmogorov's processes…
Once recognizing that point particles moving inside the extended version of the rippled billiard perform L\'evy flights characterized by a L\'evy-type distribution $P(\ell)\sim \ell^{-(1+\alpha)}$ with $\alpha=1$, we derive a generalized…