1. Introduction and review. 2. Markov chains: first steps. 3. Markov chains for the long term. 4. Branching processes. 5. Markov chain Monte Carlo. 6. Poisson process. 7. Continuous-time Markov chains. 8. Brownian motion. 9. A gentle introduction to stochastics calculus. A. Getting started with. B. Probability review. C. Summary of common probability distributions. D. Matrix algebra review. Answers to selectec odd-numbered exercices.

1. Introducción y revisión. 2. Cadenas de Markov: primeros pasos. 3. Cadenas de Markov a largo plazo. 4. Procesos de bifurcación. 5. La cadena de Markov Monte Carlo. 6. Proceso de Poisson. 7. Cadenas de Markov de tiempo continuo. 8. Movimiento browniano. 9. Una suave introducción al cálculo estocástico. A. Empezando con. B. Revisión de probabilidad. C. Resumen de las distribuciones de probabilidad comunes. D. Matrix revisión de álgebra. Respuestas a los ejercicios de número impar selectec.

Sistemas

Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations.

Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features:

• More than 200 examples and 600 end-of-chapter exercises
• A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra
• Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus
• Introductions to mathematics as needed in order to suit readers at many mathematical levels
• A companion web site that includes relevant data files as well as all R code and scripts used throughout the book.

Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.