Distribuzione congiunta di Tempi di Prima Uscita di un processo di Wiener multidimensionale con salti: applicazione alle Neuroscienze

In this thesis we studied a neuronal modeling problem, a bivariate Wiener process with two independent components and an attempt of studying its extension to three dimensions. Each component evolves independently until one of them reaches a threshold value. If the first component crosses the threshold value, it is reset while the dynamics of the other components remain unchanged. But, if this happens to the second (or third) component, the first one has a jump of constant amplitude; the second (and/or the third) component is then reset to its starting value and its evolution restarts. All the processes evolve once again until one of them reaches again its boundary. In this work, the connection among the first exit times of the two or three processes is studied.