Chemical Engineering

Introduction to probability theory: events and probability measures, conditional probabilities and the Bayes theorem; random variables, probability distributions, joint distributions, functions of random variables. Expected value and second moments, covariance matrices. Limit theorems and applications: central limit theorem, convergence in probability, law of large numbers. Markov chains: Chapman-Kolmogorov equations and classification of states, limit theorems, transitions among classes, branching processes, applications of Markov chains; time-reversible Markov chains, semi-Markov processes; continuous time Markov chains, the Kolmogorov differential equations, limiting probabilities, time reversibility. The Poisson process: interarrival and waiting time distribution, non-homogeneous Poisson process.

Author: Sheldon M. Ross Title: Stochastic Processes, 2nd Edition Editor: Wiley