Diffusion processes on graphs and the averaging principle
Some examples of asymptotic problems leading to diffusion processes on graphs are discussed. A general technique for this kind of problems is developed. The approach uses the martingale-problem method, adapted to fit non-differentiable structures. The problems considered include processes with a fast discrete component, diffusions in narrow tubes, and small random perturbations of Hamiltonian systems.
small random perturbations of Hamiltonian systems
scientific article; zbMATH DE number 528639