Belluccini, Giulia (2017) Hawkes processes and their application to neuronal networks. [Magistrali biennali]
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Hawkes processes make up the core of the present work, which is structured as follows. In Chapter 1 we have collected all that notions which have enabled us to define a Hawkes process. In particular, we have introduced here point processes with their compensator and Poisson random measures. Chapter 2 is dedicated to the definition of Hawkes processes and the presentation of some results, which ensure their existence and uniqueness under suitable assumptions. The application of Hawkes processes to neuronal networks is precisely the object of Chapter 3 and Chapter 4.
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