Sumários
Aula 4
7 março 2017, 13:30 • Ana Maria Santos Ferreira Gorjão Henriques
Exercises 1. and 5. Continuation of distributional properties of non-homogeneous Poisson process.
Refs: Sect. 5.4.1 in Ross (Probab. Models 10th ed.), Sect. 2.4 in Ross (Stoch. Proc. 2nd ed).
TPC: Exercises Sect.2.1-Non-homogeneous Poisson process.
Aula 3
6 março 2017, 12:00 • Ana Maria Santos Ferreira Gorjão Henriques
Work Presentation on Homogeneous Poisson Process
Non-homogeneous Poisson process: definition and first distributional properties.
Refs: Sect. 5.4.1 in Ross, Probab. Models, 10th ed.; Sect. 2.4 in Ross, Stoch. Proc., 2nd ed.
TPC: Exercises 1. and 5.
Aula 2
21 fevereiro 2017, 13:30 • Ana Maria Santos Ferreira Gorjão Henriques
Continuation of characterizations and properties of stochastic processes: first and second order weak stationary; stationary and independent increments; finite-dimensional distributions, stationarity (in distribution) of order n and strict stationarity.
Examples and exercises: 2.,3.,7.
Bernoulli counting process: definition, binomial and hypergeometric properties, geometric and negative binomial distributions to characterize inter-arrival times.
Example and exercise 8.
TPC: Read Sect. 1.9 in Ross (1995, 2nd ed.).
Exercises: all from Sect. 1.1 and 1.2 can be done.
Aula 1
20 fevereiro 2017, 12:00 • Ana Maria Santos Ferreira Gorjão Henriques
General information on the course.
Introduction to Stochastic Processes:
Definitions: stochastic process, index and state-space sets, sample path; discrete and continuous time processes, discrete and continuous valued processes.
Characterizations of stochastic process: mean, variance, covariance and correlation functions.
Exercises: 1.a),c),d).
TPC: Read Sect. 2.9 in Ross (2010, 10th ed.), or Sect. 1.1 in Kulkarni. Exercise to do: 1.b).