Stochastic Processes

Basic information

Workload: 

60 hours

Prerequisite: 

Probability Theory

Syllabus: 

Markov chains in discrete time: Recurrence, Transience, Stationary distribution. Poisson process and generalizations. Markov chains in continuous time: modeling, Kolmogorov equations. Martingal: definition, downtime, convergence. Brownian movement: definition, properties, Gaussian processes. Simulation techniques.

 

Teaching Plan

Bibliography

Mandatory: 

•    Ross, Sheldon. Introduction to Probability Models. John Wiley.
•    Fernandez, Pedro, Introduction to Stochastic Processes. IMPA.
•    Alencar, Marcelo Sampaio. Probability and Stochastic Processes. Publisher Erica.
 

Complementary: 

•    Lefebvre, Mario. Applied stochastic processes. Springer.
•    Palmer, T; William P. Stochastic Physics and Climate Modeling. Cambridge.
•    Chung, Kai Lai. Elementary probability theory: with stochastic processes and an introduction to Mathematical finance. Springer.
•    Varadhan, S. R. S. Stochastic processes. American Mathematical Society.
•    Chorin, Alexandre Joel. Stochastic tools in mathematics and science. Springer.