### Sumários

##### Aula 23

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

Presentation of Work 10 - Brownian Motion

Queueing theory: systems M/M/m, exercise 12; M/M/infinite, exercise 14; M/M/m/m, exercise 15. Main properties in queuing theory: PASTA and Little's law.

Refs: Sects. 8.1-8.3 in Ross (Probab. Models 10th ed.).

Note: Additional exercises for branching processes can be solved during extra-hours, Fridays 16h-18h. Short solutions will be added to the ExercisesISP document available in Fenix.

##### Aula 22

29 Maio 2017, 12:00 • Ana Maria Santos Ferreira Gorjão Henriques

Presentation of Work 14 - Applications of Markov Processes to Chemistry

Queueing theory: introduction and main performance measures in equilibrium.

System M/M/1: distribution of performance measures; exercise 12.

Refs: Sects. 8.1-8.3 in Ross (Probab. Models 10th ed.).

##### Aula 22

23 Maio 2017, 13:30 • Ana Maria Santos Ferreira Gorjão Henriques

Presentation of Work 9 - Branching processes and Work 13 - Applications to Finance

Continuous Time
Markov Chains: limiting probabilities and balance equations; exercise 6; birth-death processes.

Refs:
Sect. 6.5 in Ross (Probab. Models 10th ed.), Sect. 5.5 in Ross
(Stoch. Proc. 2nd ed).

##### Aula 21

22 Maio 2017, 12:00 • Ana Maria Santos Ferreira Gorjão Henriques

Continuous Time
Markov Chains: classification of states, Kolmogorov's differential equations and rate matrix.

Example: homogeneous Poisson process.

Birth-death processes.

Refs:
Sects. 6.3-6.4 in Ross (Probab. Models 10th ed.), Sects. 5.3-5.4 in Ross
(Stoch. Proc. 2nd ed).

##### Aula 20

16 Maio 2017, 13:30 • Ana Maria Santos Ferreira Gorjão Henriques

Presentation of W7 - DTMC and Bayesian Filter.

Continuous Time Markov Chains: Introduction, Markovian property, general definitions and framework, Transition Probability Matrix. Exercise 2.

Refs: Sects. 6.1-6.2 in Ross (Probab. Models 10th ed.), Sect. 5.1 in Ross (Stoch. Proc. 2nd ed), Sects. 5.1-5.3 in Kulkarni (1995).