Related papers: Canonical spectral representation for exchangeable…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
A theoretical analysis is presented for turbulent flows, applicable for canonical (channel, boundary-layer and free jet) geometries. Momentum and energy balance for a control volume moving at the local mean velocity decouples the…
We study stochastic sequences $\xi(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering…
A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another is a so-called coboundary. Such a representation can be used for proving some…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often…
In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…
The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…
Methods are developed for checking and completing systems of bivariate and multivariate Kendall's tau concordance measures in applications where only partial information about dependencies between variables is available. The concept of a…
Canonical systems in $\mathbb{R}^2$ with absolutely continuous real symmetric $\pi$-periodic potentials matrices are considered. A through analysis of the discriminant is given along with the indexing and interlacing of the eigenvalues of…
In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary process $W(t),t\in R$ as $$\mathcal{H}_W^\delta= \lim_{T\to\infty} T^{-1} E{ \left(\sup_{t\in \delta Z \cap [0,T]}…
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
Hoeffding-type exponential inequalities are obtained for the distribution tails of canonical von Mises' statistics of arbitrary order based on samples from a stationary sequence of random variables satisfying the {\varphi}-mixing condition.…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…
We study a new random matrix ensemble $X$ which is constructed by an application of a two dimensional linear filter to a matrix of iid random variables with infinite fourth moments. Our result gives asymptotic lower and upper bounds for the…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…