Mixed Limit Theorems for Pattern Analysis

Limit Theorems for Mixed Max–sum Processes with Renewal Stopping

This article is devoted to the investigation of limit theorems for mixed max–sum processes with renewal type stopping indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems. 1. Introduction. The main object of this article is the derivation of a number of limit theorems for mixed max–sum processes with renewal stopping. Such processes are constructed ...

Pattern theorems, ratio limit theorems and Gumbel maximal clusters for random fields

We study occurrences of patterns on clusters of size n in random fields on Z. We prove that for a given pattern, there is a constant a > 0 such that the probability that this pattern occurs at most an times on a cluster of size n is exponentially small. Moreover, for random fields obeying a certain Markov property, we show that the ratio between the numbers of occurrences of two distinct patter...

Limit theorems for mergesort

Central and local limit theorems (including large deviations) are established for the number of comparisons used by the standard top-down recursive mergesort under the uniform permutation model. The method of proof utilizes Dirichlet series, Mellin transforms and standard analytic methods in probability theory.

Limit Theorems for Bivariate Appell

Consider the stationary linear process X t = P 1 u=?1 a(t?u) u , t 2 Z, where f u g is an i.i.d. nite variance sequence. The spectral density of fX t g may diverge at the origin (long-range dependence) or at any other frequency. Consider now the quadratic form Q N = P N t;s=1 b(t ? s)P m;n (X t ; X s), where P n;m (X t ; X s) denotes a non-linear function (Appell polynomial). We provide general...

Local Limit Theorems for Free