PT EN

Probability and Stochastic Processes

Program

1 Preliminaries
1.1 Probability spaces
1.2 Integration
1.3 Absolute continuity
1.4 Notions of convergence and Slutsky's theorem
2 Random variables and Stochastic processes
2.1 Distributions and Skhorokhod's representation
2.2 Kolmogorov's existence theorem
2.3 Independence
2.4 Borel-Cantelli Lemmas
2.5 Kolmogorv's 0-1 Law
2.4 Conditional expectation
3 Martingales
3.1 Definitions and properties
3.2 Stopping times and inequalities
3.3 (Sub)martingale convergence theorem
3.4 Central limit theorem
3.5* Application to mixing stationary processes (the Gordin approximation)
4 Brownian motion
4.1 Continuity of paths and their irregularity
4.2 Strong Markov property and reflection principle
4.3 Skorohod's Embedding
5 Weak convergence
5.1 Portmanteau theorem
5.2 Tightness and Prokhorov's theorem
5.3 Weak convergence in C[0,1]
5.4 Donsker's theorem and Invariance principle

Research and Events

Events

  • Research Seminar Program (RSP)
    2017/18 second session
    Room 2.5, DMat UC
    March 9, 2018
  • PhD Defense
    Muhammad Ali Khan - Statistical instability in chaotic dynamics
    Room 031, Dep. Mathematics, Univ. Porto
    March 9, 2018
  • PhD Defense
    Anderson Feitoza Leitão Maia - Sharp regularity for the inhomogeneous porous medium equation
    14:30 - Sala dos Capelos, Univ. Coimbra
    March 21, 2018
More Events

Defended Theses

  • Forward-backward stochastic differential equations and applications
      Rui Manuel Tavares Pinto de Sá Pereira (January 2018)
      Evelina Shamarova
      Margarida Brito
  • Pseudomonads and descent
      Fernando Lucatelli Nunes (January 2018)
      Maria Manuel Clementino
  • Descent theory of (T,V)-categories: global-descent and étale-descent
      Pier Giorgio Basile (September 2017)
      Maria Manuel Clementino
More Theses