First passage time of a Markov chain that converges to Bessel process. (English) Zbl 1470.60205

Summary: We investigate the probability of the first hitting time of some discrete Markov chain that converges weakly to the Bessel process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions are computed explicitly. Furthermore, we show that the quantities that we obtained tend (with the Euclidian metric) to the corresponding ones for the Bessel process.


60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J60 Diffusion processes
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