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Feb 18, 2016 at 11:13 comment added Sosha @SamratMukhopadhyay: Unlike submarttingale, Markov chain sampled at increasing stopping times may not be a Markov Chain. And the proof you told depends on this heavily.
Feb 18, 2016 at 9:19 comment added Samrat Mukhopadhyay You could benefit by looking at the Doob's martingale inequality. You can look at its proof to see if you can do something similar for Markov processes, though I am not sure if it will be fruitful.
Feb 18, 2016 at 8:49 comment added Sosha @oferzeitouni: Thanks. That is ok. I am not asking for general case. Can you please give me some references ?
Feb 18, 2016 at 8:48 comment added ofer zeitouni certainly not - there are zero mean MC's. You need to assume more, either higher moments or something about the state space.
Feb 18, 2016 at 8:23 history asked Sosha CC BY-SA 3.0