This book presents the basic
ideas of the subject and its application to a wider audience. Topics covered
includes: The Ising model, Markov fields on graphs, Finite lattices, Dynamic
models, The tree model and Additional applications.
The contents include:
Introduction, Preliminary Results, Distributions, Random Variables,
Expectation, Independence, Weak Law of Large Numbers, Borel-Cantelli Lemmas,
Strong Law of Large Numbers, Random Series, Weak Convergence, Characteristic
Functions, Central Limit Theorems, Poisson Convergence, Stein's Method,
Random Walk Preliminaries, Stopping Times, Recurrence, Path Properties, Law
of The Iterated Logarithm.
contents include: Combinatorics, Axioms of Probability, Independence,
Conditional Probability and Independence, Random Variables, Some Discrete
Distributions, Continuous Random Variable, Normal Distributions, Normal
approximations to the binomial, Some continuous distributions, Multivariate
distributions, Expectations, Moment generating functions, Limit Laws.
These notes are intended to
give a solid introduction to Probability Theory with a reasonable level of
mathematical rigor. Topics covered includes: Elementary probability,
Discrete-time finite state Markov chains, Existence of Markov Chains,
Discrete-time Markov chains with countable state space, Probability triples,
Limit Theorems for stochastic sequences, Moment Generating Function, The Central
Limit Theorem, Measure Theory and Applications.
This book covers the following
topics: Basic Concepts of Probability Theory, Random Variables, Multiple Random
Variables, Vector Random Variables, Sums of Random Variables and Long-Term
Averages, Random Processes, Analysis and Processing of Random Signals, Markov
Chains, Introduction to Queueing Theory and Elements of a Queueing System.