Related papers: Polynomial Tail Decay for Stationary Measures

We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials

Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…

We obtain first decay rates of probabilities of tails of multivariate polynomials built on independent random variables with heavy tails. Then we derive stable limit theorems for nonconventional sums of the form $\sum_{Nt\geq n\geq…

We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the centered independent ones.

We study behavior of a measure on $[0,\infty)$ by considering its Laplace transform. If it is possible to extend the Laplace transform to a complex half-plane containing the imaginary axis, then the exponential decay of the tail of the…

This work studies the tail exponents for the height function of the stationary stochastic six vertex model in the moderate deviations regime. For the upper tail of the height function we find upper and lower bounds of matching order, with a…

In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…

In this paper we obtain the non-asymptotic exact moment and tails estimates for polynomial on martingale differences. We give also some examples on order to show the exactness of obtained results.

We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.

In this paper, it is shown that every polynomial function is mixed monotone globally with a polynomial decomposition function. For univariate polynomials, the decomposition functions can be constructed from the Gram matrix representation of…

The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain properties of the tail process and establish new ones. A new formulation of the time change…

Exponential tail bounds for sums play an important role in statistics, but the example of the $t$-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns…

We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows…

This article concerns the tail probabilities of a light-tailed Markov-modulated L\'evy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of…

The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

We prove that the random variable $\ct=\argmax_{t\in\rr}\{\aip(t)-t^2\}$ has tails which decay like $e^{-ct^3}$. The distribution of $\ct$ is a universal distribution which governs the rescaled endpoint of directed polymers in 1+1…

We consider a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) $\{(\boldsymbol{X}_n,J_n)\}$ on $\mathbb{Z}_+^2\times S_0$, where $\boldsymbol{X}_n=(X_{1,n},X_{2,n})$ is the level state, $J_n$ the phase…

We study the shape of the tail of a heap of granular material. A simple theoretical argument shows that the tail adds a logarithmic correction to the slope given by the angle of repose. This expression is in good agreement with experiments.…

A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic…