From diffusions on graphs to Markov chains via asymptotic state lumping
We show that fast diffusions on finite graphs with semi permeable membranes on vertices may be approximated by finite-state Markov chains provided the related permeability coefficients are appropriately small. The convergence theorem involves a singular perturbation with singularity in both operator and boundary/transmission conditions, and the related semi groups of operators converge in an irregular manner. The result is motivated by recent models of synaptic depression.
scientific article; zbMATH DE number 6085741
scientific article