Convergence In Distribution Of Sums Research Articles

Invariant Measure and a Limit Theorem for Some Generalized Gauss Maps

Continued fractions w.r.t. a specified class of numbers is considered. The invariant measures of the corresponding transformations are identified connecting the continued fractions with geodesics on the upper half plane. A problem of convergence in distribution of sums of the coefficients of the continued fraction is also considered.

Generalized Poisson Distributions as Limits of Sums for Arrays of Dependent Random Vectors

Arrays of random vectors with values in Rd stationary in rows, are investigated. By the assumptions related to the ones used in the extreme value theory a limit thoerem for sums is proved. Necessary and sufficient conditions for the convergence in distribution of sums to some generalized Poisson distributions in m-dependent and α-, ρ-, φ-mixing cases are given. As a tool the point processes theory is used.

Intermediate sums and stochastic compactness of maxima

A connection between the convergence in distribution of sums of intermediate order statistics and the stochastic compactness of maxima is established.

Convergence in distribution of sums of bivariate Appell polynomials with long-range dependence

Normalized quadratic forms of moving averages converge to double Wiener-Ito integrals if the summands are sufficiently dependent. This result extends to sums of bivariate Appell polynomials of arbitrary degree.

Poisson theorem for non-homogeneous Markov chains

This paper gives necessary and sufficient conditions for the convergence in distribution of sums of the 0–1 Markov chains to a compound Poisson distribution.

Poisson theorem for non-homogeneous Markov chains

This paper gives necessary and sufficient conditions for the convergence in distribution of sums of the 0–1 Markov chains to a compound Poisson distribution.

Thinning of Cluster Processes: Convergence of Sums of Thinned Point Processes

This is a study of the convergence in distribution of sums of dependent point processes that are becoming uniformly sparse due to a thinning operation. Under this operation, each point process is randomly deleted or retained depending on its structure, and when a process is retained, each of its points is deleted or retained depending on its location and the structure of the process. Such a sum can be interpreted as a thinned cluster process: the residual of a cluster process after its cluster origins and single points have been thinned. Our main result gives a necessary and sufficient condition for the sums to converge and states that their limit must be a Cox process (a Poisson process with a random intensity measure). This result has some parallels to the classical result on the convergence of sums of independent point processes to a Poisson process, and it contains Kallenberg's result on the convergence of a thinned point process to a Cox process. Corollaries are presented for the cases in which the processes being summed are either independent or satisfy a weak law of large numbers before they are thinned. In addition, sufficient conditions are given for sums of randomly selected processes, with no single point deletions, to converge to infinitely divisible point processes or to mixtures of these processes.

Some properties of convergence in distribution of sums and maxima of dependent random variables

Some properties of convergence in distribution of sums and maxima of dependent random variables