| Abstract: |
| In this talk, we consider a sequence of Markov chains defined on point sets in a Euclidean domain and discuss sufficient conditions for its subsequential limits to possess the Markov property. Establishing the Markov property is important, as it implies that the limit generates a symmetric Dirichlet form under appropriate additional conditions including the symmetry of each chain, which in turn allows for characterizing the limit through concepts such as the Silverstein extension. We also discuss conditions under which the subsequential limit becomes a reflected Brownian motion on the domain, as well as a framework applicable to more general Markov processes. |
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