Topics in Piecewise Deterministic Markov Processes with Applications to Neuron Models
Sprache des Vortragstitels:
Englisch
Original Kurzfassung:
I will first give a brief motivation form mathematical neuroscience. Then focus of the talk will be on hybrid stochastic models, in particular Piecewise Deterministic Markov Models, which represent the class of models for single neurons or neuronal membranes, respectively, closest to the biophysical reality and, on a larger scale, still analytically and numerically tractable. These models arise from coupling a continuous-time discrete Markov model with a finite- or infinite-dimensional deterministic dynamical model of a macroscopic variable. In the second part, I want to discuss on the one hand, a Law of Large Numbers for PDMPs that connect the stochastic processes to macroscopic deterministic models. On the other hand. I will present numerical approaches to the strong pathwise simulation of PDMPs. For the numerics I will present analytical as well as numerical results.
Forschungs-