Class 20

26 Novembro 2012, 11:00 • MARIA DE LURDES CARAÇAS CENTENO

8. CONTINUOUS TIME HOMOGENEOUS MARKOV CHAINS

8.1. Introduction: time homogeneous Markov process; Chapman-Kolmogorov equations

8.2. The transition probability matrix

8.3. The forward and backward differential equations

 

 

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Class 19

21 Novembro 2012, 11:00 • MARIA DE LURDES CARAÇAS CENTENO

Exercises.

 

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Class 18

19 Novembro 2012, 11:00 • MARIA DE LURDES CARAÇAS CENTENO

7.2. The homogeneous Poisson process: the gamma, the binomial and the uniform

7.3. The non-homogeneous Poisson process

7.4. The mixed Poisson process; the Polya process

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Class 17

14 Novembro 2012, 11:00 • MARIA DE LURDES CARAÇAS CENTENO

7. INTRODUCTION TO COUNTING PROCESSES

7.1. Some definitions: counting process, Markov counting process, birth process - the homogeneous and the non-homogeneous processes

7.2. The homogeneous Poisson process: its genesis, discussion of the postulates

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Class 16

12 Novembro 2012, 11:00 • MARIA DE LURDES CARAÇAS CENTENO

6.4. Classification of states

6.5. Limit Behaviour

6.6. Applications to no claim discount and bonus-malus systems

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