Upper Escape Rate for Weighted Graphs via Metric Graphs

摘要

The upper escape rate for a Markov process is a natural partial generalization of the celebrated Khintchine's law of the iterated logarithm. In this article, we present a new proof of the sharp volume growth criterion for upper escape rate of continuous time random walks on weighted graphs in Huang and Shiozawa (Stoch. Process Appl. 124(1), 317-347 2014). Our proof is based on comparison with a corresponding modified metric graph, and this technique allows us to remove the restriction on vertex weight in Huang and Shiozawa (Stoch. Process Appl. 124(1), 317-347 2014) as well.