Related papers: Tail indices for AX+B recursion with triangular ma…

The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…

Long Memory Stochastic volatility (LMSV) models capture two standardized features of financial data: the log-returns are uncorrelated, but their squares, or absolute values are (highly) dependent and they may have heavy tails. EGARCH and…

We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.

We generalize regular subdivisions (polyhedral complexes resulting from the projection of the lower faces of a polyhedron) introducing the class of recursively-regular subdivisions. Informally speaking, a recursively-regular subdivision is…

This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in "User-friendly tail bounds for sums of random matrices" (arXiv:1004.4389v6) that yields both upper…

This survey paper introduces to a technique called Torsion Subcomplex Reduction (TSR) for computing torsion in the cohomology of discrete groups acting on suitable cell complexes. TSR enables one to skip machine computations on cell…

Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…

We study the random variables (r.v.) with values in the so-called mixed (anisotropic) Lebesgue-Riesz spaces: formulate the sufficient conditions for belonging of the r.v. to these spaces, estimate the tail of norms distribution, especially…

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…

We provide a generalisation of Pinelis' Rademacher-Gaussian tail comparison to complex coefficients. We also establish uniform bounds on the probability that the magnitude of weighted sums of independent random vectors uniform on Euclidean…

Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. In this paper, we use the concept of sparse regular variation introduced by Meyer and Wintenberger (2021)} to infer the tail…

The expressions of solutions for general $n\times m$ matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential…

Vertically symmetric alternating sign matrices (VSASMs) of order $2n+1$ are known to be equinumerous with lozenge tilings of a hexagon with side lengths $2n+2$, $2n$, $2n+2$, $2n$, $2n+2$, $2n$ and a central triangular hole of size $2$ that…

We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," along with investigation of their properties. A recursive PRS is defined as, if there exists the GCD (greatest common divisor) of initial…

Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…

In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…

We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and…

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

This work investigates the tail behavior of solutions to the affine stochastic fixed-point equation of the form $X\stackrel{d}{=}AX+B$, where $X$ and $(A,B)$ are independent. Focusing on the light-tail regime, following [Burdzy et al.…

Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…