Some theorems in probability theory

Limit Theorems in Free Probability Theory. Ii

Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line R+ and on the unit circle T we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.

Some Theorems on the Algorithmic Approach to Probability Theory and Information Theory

The dissertation uses the terms and notation in paper [6] that is attached to [Russian original of] this text. The paper also contains figures referred to in the text of the dissertation as well as the index. We consider strings in the alphabet {0, 1}, i.e., finite sequences of zeroes and ones in a 1-1 correspondence with natural numbers: 1 Λ ↔ 0 0 ↔ 1

Some notes on asymptotic theory in probability

We provide a precise account of some commonly used results from asymptotic theory in probability.

Some Concepts in Probability and Information Theory

Fe b 20 06 LIMIT THEOREMS IN FREE PROBABILITY THEORY

Based on a new analytical approach to the definition of additive free con-volution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical Probability Theory.