Stochastic Processes

Segundas e Quartas de 16:20h às 18h (Zoom). Monitoria: TBA
Syllabus

Discrete-time Markov chains. Discrete-time martingales. Continuous-time Markov chains. Poisson process. Birth and death process. Gaussian process. Brownian motion. Stochastic calculus: Itô integral and Itô formula.

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If we have time:  Queueing theory. Renewal process.

Bibliography

  • Grimmett, G. R. and Stirzaker, D. R.  (2001). Probability and Random Processes.  Oxford.

  • Steele , J. M. (2012). Stochastic Calculus and Financial Applications . Springer. 

  • Hoel, P., Port, S. and Stone, C. (1986). Introduction to Stochastic Processes. Waveland.

  • Berestycki, N. and Sousi. P. (2017). Applied Probability. Lecutre notes.

Provas e Avisos

  • Aulas começam dia 14/6 e o link do Zoom será enviado aos alunos inscritos.

  • Avaliação: duas provas (P1 e P2) e a média final será M = (P1 + P2)/2

  • P1: 21/7 e P2: 1/9

  • As provas serão liberadas pelo eclass e os alunos terão 24h até a entrega pelo sistema.

Lecture notes:
Homework:

  • Probability

  • Markov chains

  • Queueing and Renewal

  • Conditional expectation

  • Martingales

  • Brownian motion