On the Homogenization of Diffusions in Periodic Comb-Like Structures

In this thesis we study the homogenization of diffusions in two particular comb-like structures. In both models, the comb can be viewed as a macroscopic diffusion with
a trapping mechanism. The processes spend non-trivial amounts of time in these traps and convergence is established using martingale problems and excursion theory. The limiting process has an explicit form as time-changed Brownian motion and also as the unique solution to a certain system of SDE. The limiting macroscopic
process is also shown to be a trapped diffusion whose Kolmogorov equation has a term with fractional-time derivatives.