STOCHASTIC MODELLING AND SIMULATION

1. Discrete state spae stochastic modelling. Markov chains in discrete and continuous time, discrete event simulation, population models. Continuous space-discrete time MArkov Processes 2. Continuous stochastic modeling: Stochastic Differential Equations (SDEs), Numerical Algorithms for SDEs, Fokker Planck Equation, Ito and Stratonovich SDEs, Noise-Induced Transitions, Bounded Stochastic Processes, Nonlinear Fokker-Planck Equation as Model of Phase Transitions 3. Stochastic approximations: mean field, Langevin approximation, hybrid approximations. 4. Parameter estimation, ABC method and system design. Examples from systems biology, epidemiology, statistical physics, performance of computer networks, ecology.

Discipline matematiche, fisiche e informatiche