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First hitting problems for Markov chains that converge to a geometric Brownian motion

Mario Lefebvre, Moussa Kounta

Article (2011)

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Abstract

We consider a discrete-time Markov chain with state space {1,1+∆x,...,1+k∆x = N}. We compute explicitly the probability pj that the chain, starting from 1 + j∆x, will hit N before 1, as well as the expected number dj of transitions needed to end the game. In the limit when ∆x and the time ∆t between the transitions decrease to zero appropriately, the Markov chain tends to a geometric Brownian motion. We show that pj and dj∆t tend to the corresponding quantities for the geometric Brownian motion.
Subjects: 3000 Statistics and probability > 3007 Stochastic processes
3000 Statistics and probability > 3008 Applied probability
Department: Department of Mathematics and Industrial Engineering
PolyPublie URL: https://publications.polymtl.ca/4995/
Journal Title: ISRN Discrete Mathematics (vol. 2011)
Publisher: Hindawi
DOI: (10.5402/2011/346503)
Official URL: https://www.hindawi.com/journals/isrn/2011/346503/
Date Deposited: 06 Nov 2020 12:26
Last Modified: 11 Nov 2022 13:56
Cite in APA 7: Lefebvre, M., & Kounta, M. (2011). First hitting problems for Markov chains that converge to a geometric Brownian motion. ISRN Discrete Mathematics, 2011, 346503. https://www.hindawi.com/journals/isrn/2011/346503/

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