Advanced Probability

Probability spaces. Random variables. Independence. Borel-Cantelli Lemmas. Weak and strong law of large numbers. Iterated Logarithm Law. Birkhoff's Ergodic Theorem. Convergence in distribution. Continuous mapping theorem. Characteristic function. Central Lindenberg-Feller Limit Theorem. Stable distributions. Conditional hope. Conditional probability.

 

Basic Information

Workload
45 hours
Requirements
Measure and Integration

Mandatory:

  • Athreya, K. B., & Lahiri, S. N. (2006). Measure theory and probability theory. Springer Science & Business Media.
  • Rosenthal, J. S. (2006). A first look at rigorous probability theory. World Scientific Publishing Company.
  • Williams, D. (1991). Probability with martingales. Cambridge university press.

Complementary:

  • Durrett, R. (2019). Probability: theory and examples (Vol. 49). Cambridge university press.
  • Billingsley, P. (2008). Probability and measure. John Wiley & Sons.
  • Bartle, R. G. (2014). The elements of integration and Lebesgue measure. John Wiley & Sons.
  • Pedro J. Fernandez. Medida e Integração. Coleção Euclides, IMPA.