Related papers: Packing Dimension Profiles and Levy Processes
Dimension profiles were introduced by Falconer and Howroyd to provide formulae for the box-counting and packing dimensions of the orthogonal projections of a set E or a measure on Euclidean space onto almost all m-dimensional subspaces. The…
In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\rm Dim}_s$ that are parametrized by real numbers $s>0$. Subsequently, Howroyd (2001)…
Dimension profiles were introduced in [8,11] to give a formula for the box-counting and packing dimensions of the orthogonal projections of a set $R^n$ onto almost all $m$-dimensional subspaces. However, these definitions of dimension…
We use the recently-developed multiparameter theory of additive Levy processes to establish novel connections between an arbitrary Levy process $X$ in $\mathbf{R}^d$, and a new class of energy forms and their corresponding capacities. We…
We prove uniform Hausdorff and packing dimension results for the inverse images of a large class of real-valued symmetric L\'evy processes. Our main result for the Hausdorff dimension extends that of Kaufman (1985) for Brownian motion and…
We consider several classical results related to the Hausdorff dimension of exceptional sets of orthogonal projections and try to find out whether they have reasonable formulations in terms of packing dimension. We also investigate the…
We study the Macroscopic Hausdorff dimension of the upper and lower level sets of the Airy processes, following the general method developed in Khoshnevisan et al. \cite{KKX17}. For the Airy$_1$ process, the approach to macroscopic…
In this paper we prove uniform Hausdorff and packing dimension results for the images of a large family of Markov processes. The main tools are the two covering principles of Xiao (second author). As applications, uniform Hausdorff and…
We establish an other upper bounding for packing dimension in the framework of the vectorial multifractal formalism that is in some cases finer than that established by J. Peyriere.
Relations between so-called harness processes and initial enlargements of the filtration of a Levy process with its positions at fixed times are investigated.
This paper is about lower and upper bounds for the Hausdorff dimension of the level and collision sets of a class of Feller processes. Our approach is motivated by analogous results for L\'evy processes by Hawkes (for level sets), Taylor…
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…
In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…
We study the sets of points where a L\'evy function and a translated L\'evy function share a given couple of H\''older exponents, and we investigate how their Hausdorff dimensions depend on the translation parameter.
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…
We compute the Hausdorff dimension of the zero set of an additive Levy process.
We derive characteristic function identities for conditional distributions of an r-trimmed Levy process given its r largest jumps up to a designated time t. Assuming the underlying Levy process is in the domain of attraction of a stable…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
We study the packing dimension of Borel measures under orthogonal projections. We give a necessary and sufficient condition such that typical projections of Borel probability measures have full packing dimension and derive general lower…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…