Sumários

Aula 10

27 março 2017, 12:00 • Ana Maria Santos Ferreira Gorjão Henriques

Presentation of W5 on Compound Poisson process.
Renewal processes: one-to-one correspondence between the renewal function and the inter-renewal distribution. Exercise 8.
Recurrence times: age and residual life at time t; exercise 16.
Ref. 7.3 in Ross (Probab. Models 10th ed.).

Aula 8

21 março 2017, 13:30 • Ana Maria Santos Ferreira Gorjão Henriques

Renewal processes: first distributional properties, and mean value function. Asymptotic properties.
Exercises 11 and 13.

Refs for this first part on renewal processes:
Sects. 7.1--7.3 in Ross (Probab. Models 10th ed.), Sects. 3.1--3.3 in Ross (Stoch. Proc. 2nd ed).

Aula 7

20 março 2017, 12:00 • Ana Maria Santos Ferreira Gorjão Henriques

Properties of compound Poisson processes: selection, asymptotic normality and sum of independent compound Poisson processes.

W3 on non-homogeneous Poisson processes by Ana Carolina Fonseca.

Counting processes and renewal processes: introduction.
Exercises 1 and 5.

Aula 6

14 março 2017, 13:30 • Ana Maria Santos Ferreira Gorjão Henriques

Conditional probabilities and expectations: stopping time and Wald's equation. Exercises 13 and 14.
Conditional and Compound Poisson processes: definitions, main properties, exercises with applications 12, 17(a,b) and 18.

Refs for Conditional Poisson processes: Sect. 5.4.3 in Ross (Probab. Models 10th ed.), Sect. 2.6 in Ross (Stoch. Proc. 2nd ed).
Refs for Compound Poisson processes: Sect. 5.4.2 in Ross (Probab. Models 10th ed.), Sect. 2.5.2 in Ross (Stoch. Proc. 2nd ed).

TPC: Finish exercises 17 and 18.

Aula 5

13 março 2017, 12:00 • Ana Maria Santos Ferreira Gorjão Henriques

Distributions of inter-event times and joint n-th successive time-events in the non-homogeneous Poisson process, and relation with order statistics and homogeneous Poisson process.
Conditional probabilities and expectations: definitions and properties.
Exercise 12.

Refs for conditional probability, conditional expectation, moment generating function and probability generating function: Chapter 3 in Ross (Probab. Models 10th ed.), Sects 1.4, 1.5 in Ross (Stoch. Proc. 2nd ed).