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First Hitting Problems for Markov Chains That Converge to a Geometric Brownian Motion
Joint Authors
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-11
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We consider a discrete-time Markov chain with state space {1,1+Δx,…,1+kΔx=N}.
We compute explicitly the probability pj that the chain, starting from 1+jΔx, will hit N before 1, as well as the expected number dj of transitions needed to end the game.
In the limit when Δx and the time Δt between the transitions decrease to zero appropriately, the Markov chain tends to a geometric Brownian motion.
We show that pj and djΔt tend to the corresponding quantities for the geometric Brownian motion.
American Psychological Association (APA)
Lefebvre, Mario& Kounta, Moussa. 2011. First Hitting Problems for Markov Chains That Converge to a Geometric Brownian Motion. ISRN Discrete Mathematics،Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-464569
Modern Language Association (MLA)
Lefebvre, Mario& Kounta, Moussa. First Hitting Problems for Markov Chains That Converge to a Geometric Brownian Motion. ISRN Discrete Mathematics No. 2011 (2011), pp.1-15.
https://search.emarefa.net/detail/BIM-464569
American Medical Association (AMA)
Lefebvre, Mario& Kounta, Moussa. First Hitting Problems for Markov Chains That Converge to a Geometric Brownian Motion. ISRN Discrete Mathematics. 2011. Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-464569
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-464569