Related papers: A Lundberg-type inequality for an inhomogeneous re…
Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…
Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov…
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other…
Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.
We provide an inequality which is a useful tool in studying both large deviation results and limit theorems for sums of random fields with "negligible" small values. In particular, the inequality covers cases of stable limits for random…
In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field…
Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $\alpha\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate…
We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…
In this paper we prove a special case of the Lehmer inequality for Drinfeld modules. Also, based on this inequality, we prove certain Mordell-Weil type of theorems for certain infinitely generated fields.
This paper considers a Cram\'er-Lundberg risk setting, where the components of the underlying model change over time. These components could be thought of as the claim arrival rate, the claim-size distribution, and the premium rate, but we…
A uniform key renewal theorem is deduced from the uniform Blackwell's renewal theorem. A uniform LDP (large deviations principle) for renewal-reward processes is obtained, and MDP (moderate deviations principle) is deduced under conditions…
We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…
A non-linear Black-Scholes-type equation is studied within counterparty risk models. The classical hypothesis on the uniform Lipschitz-continuity of the non-linear reaction function allows for an equivalent transformation of the semi-linear…
Dropout represents a typical issue to be addressed when dealing with longitudinal studies. If the mechanism leading to missing information is non-ignorable, inference based on the observed data only may be severely biased. A frequent…
We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles,…
We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded…
We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…
The Rotar central limit theorem is a remarkable theorem in the non-classical version since it does not use the condition of asymptotic infinitesimality for the independent individual summands, unlike the theorems named Lindeberg's and…