Stochastic Processes
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.
Basic Information
Workload
60 hours
Requirements
Probability Theory
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.