Alexis Anagnostakis:
General Diffusions on Metric Graphs as limits of Time-Space Markov Chains
Time and place
Friday, 25.7.25, 12:00-13:00, Seminarraum 404
Abstract
We introduce the Space-Time Markov Chain Approximation (STMCA) for a general diffusion process on a finite metric graph \(\Gamma\).
The STMCA is a doubly asymmetric (in both time and space) random walk defined on a subdivisions of \(\Gamma\), with transition probabilities and conditional transition times that match, in expectation, those of the target diffusion. We derive bounds on the \(p\)-Wasserstein distances between the diffusion and its STMCA in terms of a thinness quantifier of the subdivision. Additionally, (i) we present a method for constructing numerically efficient approximations with optimal convergence rates and (ii) provide explicit analytical formulas for transition probabilities and times, enabling practical implementation of the STMCA. Numerical experiments illustrate our results.