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First Passage Time of a Markov Chain That Converges to Bessel Process

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  • Moussa Kounta

Abstract

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.

Suggested Citation

  • Moussa Kounta, 2017. "First Passage Time of a Markov Chain That Converges to Bessel Process," Abstract and Applied Analysis, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlaaa:v:2017:y:2017:i:1:n:7189826
    DOI: 10.1155/2017/7189826
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    References listed on IDEAS

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    1. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," The Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
    2. Alexander Vollert, 2003. "A Stochastic Control Framework for Real Options in Strategic Evaluation," Springer Books, Springer, number 978-1-4612-2068-8, March.
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