Branching process

9 Abril 2024, 11:00 • Alessandro Margheri

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Branching processes. Problem of the extinction of a family name. Extinction within n generations, fixed points of a scalar first order recurrence equation and coweb method. Galton-Watson process.   First step to get the corresponding     probability  generating funnction

Linear birth-death processes

27 Março 2024, 10:00 • Alessandro Margheri

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Miguel: ex. 4 (part of the expected value).   End of the topic birth and death processes. Variance and coefficient of variation.  Some terminology: random variable, time continuous homogeneous Markov process.  Realization of a  stochastic process 

Linear birth death process

26 Março 2024, 11:00 • Alessandro Margheri

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Generating function and its properties.  Construction of the partial differential equation  which it must satisfy. Explicit expression of the solution. Probability of extinction, probability of ultimate  extinction, and expected value of the process. 

Compartmental models

20 Março 2024, 10:00 • Alessandro Margheri

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M-matrices. More general linear compartmental   models. Linear Birth process.

Exercises

19 Março 2024, 11:00 • Alessandro Margheri

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Dicussion of excercises 4 (Manuel) and 5 (Leonard).   Linear birth death process: deduction of the master equation from the compartmental model.