Asymptotic distribution with random indices for linear processes

Asymptotic Distribution for Random Median Quicksort

The first complete running time analysis of a stochastic divide and conquer algorithm was given for Quicksort, a sorting algorithm invented 1961 by Hoare. We analyse here the variant Random Median Quicksort. The analysis includes the expectation, the asymptotic distribution, the moments and exponential moments. The asymptotic distribution is characterized by a stochastic fixed point equation. T...

Asymptotic Distribution of Divergence Measure with Applications

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Laws of Large Numbers for Random Linear

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...

Asymptotic degree distribution in random recursive trees

The distributions of vertex degrees in random recursive trees and random plane recursive trees are shown to be asymptotically normal. Formulas are given for the asymptotic variances and covariances of the number of vertices with given outdegrees. We also give functional limit theorems for the evolution as vertices are added. The proofs use some old and new results about generalized Pólya urn mo...