Related papers: Operator Tail Densities of Multivariate Copulas
Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing…
Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…
A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…
For a bivariate probability distribution, local dependence around a single point on the support is often formulated as the second derivative of the logarithm of the probability density function. However, this definition lacks the invariance…
We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak…
We propose a new approach towards approximating the density-to-pair-density map based on copula theory from statistics. We extend the copula theory to multi-dimensional marginals, and deduce that one can describe any (exact or approximate)…
We provide exact large-time equivalents of the density and upper tail distributions of the exponential functional of a subordinator in terms of its Laplace exponents. This improves previous results on the logarithmic asymptotic behaviour of…
Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-M\'ezard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes,…
In the paper we construct the wave functional model of a symmetric restriction of the regular Sturm-Liouville operator on an interval. The model is based upon the notion of the wave spectrum and is constructed according to an abstract…
We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. A multivariate extension was established by Aulbach et al.…
We study cocycle properties of vertex operators and present an operator representation of cocycle operators, which are attached to vertex operators to ensure the duality of amplitudes. It is shown that this analysis makes it possible to…
This paper introduces a new class of Cox models for dependent bivariate data. The impact of the covariate on the dependence of the variables is captured through the modification of their copula. Various classes of well known copulas are…
We show that any finite set of linear partial differential operators with continuous coefficients is linearly dependent if and only if it is locally linearly dependent. It follows that the reflexive closure of any finite set of such…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
We propose to quantify the complexity of non-equilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of level spacing distribution of their spectra. Based on extensive numerical studies in a…
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…