Related papers: Multifractal analysis of L\'evy fields
We study homogeneous quantum L\'{e}vy processes and fields with independent additive increments over a noncommutative *-monoid. These are described by infinitely divisible generating state functionals, invariant with respect to an…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
This paper studies the local structure of continuous random fields on $\mathbb R^d$ taking values in a complete separable linear metric space ${\mathbb V}$. Extending seminal work of Falconer, we show that the generalized $(1+k)$-th order…
We introduce a deterministic model defined on a two dimensional hyperbolic lattice. This model provides an example of a non random system whose multifractal behaviour has a number theoretic origin. We determine the multifractal exponents,…
The problem of estimating the L\'evy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the…
In this paper we present some new limit theorems for power variations of stationary increment L\'{e}vy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477--4528,…
We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some L\'evy processes, and weighted fractional inequalities on irregular open…
The Levy stability analysis is carried out for e+e- collisions at Z^0 mass using Monte Carlo method. The Levy index \mu is found to be \mu=1.701 +- 0.043. The self-similar generalized dimensions D(q) and multi-fractal spectrum f(\alpha) are…
In this paper, we show new representations of one-sided L\'{e}vy stable distributions for irrational L\'{e}vy indices of the type $\left(\frac{p}{q}\right)^{\frac{l_{2}}{l_{1}}}$ which are not covered in \cite{pg1} : for rational L\'{e}vy…
We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. We focus fir st on consistent polygonal fields, for which we show Markovianity and…
This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and L\'evy processes which summarize and extend the literature on these subjects. The results surveyed include point…
In this paper we introduce a new class of L\'evy processes which we call hypergeometric-stable L\'evy processes, because they are obtained from symmetric stable processes through several transformations and where the Gauss hypergeometric…
Recent scenarios of phenomenologically realistic string compactifications involve the existence of gauge sectors localized on D-branes at singular points of Calabi-Yau threefolds. The spectrum and interactions in these gauge sectors are…
Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…
For stationary, homogeneous Markov processes (viz., L\'{e}vy processes, including Brownian motion) in dimension $d\geq 3$, we establish an exact formula for the average number of $(d-1)$-dimensional facets that can be defined by $d$ points…
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…
An extension of the Heath--Jarrow--Morton model for the development of instantaneous forward interest rates with deterministic coefficients and Gaussian as well as L\'evy field noise terms is given. In the special case where the L\'evy…
Simplicial sets generalise many categories of graphs. In this paper, we give a complete characterisation of the Lawvere-Tierney topologies on (semi-)simplicial sets, on bicolored graphs, and on fuzzy sets. We apply our results to establish…
We study the set of common F_q-rational zeros of systems of multivariate symmetric polynomials with coefficients in a finite field F_q. We establish certain properties on these polynomials which imply that the corresponding set of zeros…
We study the local regularity and multifractal nature of the sample paths of jump diffusion processes, which are solutions to a class of stochastic differential equations with jumps. This article extends the recent work of Barral {\it et…