Probability, Random Variables and Stochastic Processes

  title={Probability, Random Variables and Stochastic Processes},
  author={Athanasios Papoulis},
Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory 
Elements of Probability Theory
This chapter presents a review of some basic concepts of probability theory, including probability spaces, random variables, random matrices, distributions, densities and expectations. Some classical
Time-Dependent Random Variables: Classical Stochastic Processes
If one considers a random variable which depends on time, one is led to the concept of a stochastic process. After the definition of a general stochastic process in Sect. 5.1, we introduce the class
An Estimate of the Probability Density Function of the Sum of a Random Number N of Independent Random Variables
A new estimate of the probability density function (PDF) of the sum of a random number of independent and identically distributed (IID) random variables is shown. The sum PDF is represented as a sum
Random Variables: Fundamentals of Probability Theory and Statistics
A fundamental concept for any statistical treatment is that of the random variable. Thus this concept and various other closely related ideas are presented at the beginning of this book. Section 2.1
Random Number and Variate Generation
This chapter discusses various methods for the generation of random samples distributed according to given probability distributions, in both the univariate and multivariate cases. These methods can
On generating sets of binary random variables with specified first- and second- moments
This work proposes a low-complexity algorithm for generating sets of binary random variables with specified means and pairwise correlations, and shows that the parameters of this data-generation algorithm can be easily designed to achieve the desired statistics, under broad conditions.
On the Dimensionality of the Stochastic Space in the Stochastic Finite Element Method
In recent works concerning the solution of various kinds of random equations or the stochastic simulation of random functions often so called (generalized) polynomial chaos expansions are used.
Random Variables : An Overview
The concept of a random variable, which is nothing more than a variable whose numeric value is determined by the outcome of an experiment, is introduced and the probability distribution and probability density function are introduced.


16-1 Introduction / 16-2 Markov Processes / 16-3 Queueing Theory / 16-4 Networks of Queues
  • 16-1 Introduction / 16-2 Markov Processes / 16-3 Queueing Theory / 16-4 Networks of Queues