Related papers: Edgeworth expansions for weakly dependent random v…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
We prove that certain asymptotic moments exist for some random distance expanding dynamical systems and Markov chains in random dynamical environment, and compute them in terms of the derivatives at the $0$ of an appropriate pressure…
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow…
We consider a scheme of equiprobable allocation of particles into cells by sets. The Edgeworth type asymptotic expansion in the local central limit theorem for a number of empty cells left after allocation of all sets of particles is…
This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram\'{e}r condition in Angst…
An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given…
We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the…
In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…
Let $X=(X_1,\ldots,X_n)$ be a vector of i.i.d. random variables where $X_i$'s take values over $\mathbb{N}$. The purpose of this paper is to study the number of weakly increasing subsequences of $X$ of a given length $k$, and the number of…
We study the distribution of a general class of asymptoticallylinear statistics which are symmetric functions of $N$ independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a…
The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables…
The "typical" asymptotic behavior of the weighted sums of independent, identically distibuted random vectors in k-dimensional space is considered. It is shown that under finitnes of fifth absolute moment of an individual term the rate of…
We obtain asymptotic expansions for local probabilities of partial sums for uniformly bounded independent but not necessarily identically distributed integer-valued random variables. The expansions involve products of polynomials and…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
Regular and singular parts of asymptotic expansions of semi-Markov random evolutions are given. Regularity of boundary conditions is shown. An algorithm for calculation of initial conditions is proposed.
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…
We deduce sufficient conditions for the Central Limit Theorem (CLT) in the Lebesgue-Riesz space L(p) defined on some measure space for the sequence of centered random variables satisfying the strong mixing (Rosenblatt) condition. We…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…