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Computing lower and upper expected first passage and return times in imprecise birth-death chains

Stavros Lopatatzidis, Jasper De Bock UGent and Gert De Cooman UGent (2017) INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. 80. p.137-173
abstract
We provide simple methods for computing exact bounds on expected first-passage and return times in finite-state birth–death chains, when the transition probabilities are imprecise, in the sense that they are only known to belong to convex closed sets of probability mass functions. In order to do that, we model these so-called imprecise birth–death chains as a special type of time-homogeneous imprecise Markov chain, and use the theory of sub- and supermartingales to define global lower and upper expectation operators for them. By exploiting the properties of these operators, we construct a simple system of non-linear equations that can be used to efficiently compute exact lower and upper bounds for any expected first-passage or return time. We also discuss two special cases: a precise birth–death chain, and an imprecise birth–death chain for which the transition probabilities belong to linear-vacuous mixtures. In both cases, our methods simplify even more. We end the paper with some numerical examples.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Birth–death chain, First-passage time, Return time, Lower expectation, Imprecise probability, Submartingale
journal title
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
INT J APPROX REASON
volume
80
pages
137 - 173
Web of Science type
Article
ISSN
0888-613X
DOI
10.1016/j.ijar.2016.08.008
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
8074823
handle
http://hdl.handle.net/1854/LU-8074823
date created
2016-09-14 15:22:17
date last changed
2017-09-20 11:26:07
@article{8074823,
  abstract     = {We provide simple methods for computing exact bounds on expected first-passage and return times in finite-state birth--death chains, when the transition probabilities are imprecise, in the sense that they are only known to belong to convex closed sets of probability mass functions. In order to do that, we model these so-called imprecise birth--death chains as a special type of time-homogeneous imprecise Markov chain, and use the theory of sub- and supermartingales to define global lower and upper expectation operators for them. By exploiting the properties of these operators, we construct a simple system of non-linear equations that can be used to efficiently compute exact lower and upper bounds for any expected first-passage or return time. We also discuss two special cases: a precise birth--death chain, and an imprecise birth--death chain for which the transition probabilities belong to linear-vacuous mixtures. In both cases, our methods simplify even more. We end the paper with some numerical examples.},
  author       = {Lopatatzidis, Stavros and De Bock, Jasper and De Cooman, Gert},
  issn         = {0888-613X},
  journal      = {INTERNATIONAL JOURNAL OF APPROXIMATE REASONING},
  keyword      = {Birth--death chain,First-passage time,Return time,Lower expectation,Imprecise probability,Submartingale},
  language     = {eng},
  pages        = {137--173},
  title        = {Computing lower and upper expected first passage and return times in imprecise birth-death chains},
  url          = {http://dx.doi.org/10.1016/j.ijar.2016.08.008},
  volume       = {80},
  year         = {2017},
}

Chicago
Lopatatzidis, Stavros, Jasper De Bock, and Gert De Cooman. 2017. “Computing Lower and Upper Expected First Passage and Return Times in Imprecise Birth-death Chains.” International Journal of Approximate Reasoning 80: 137–173.
APA
Lopatatzidis, S., De Bock, J., & De Cooman, G. (2017). Computing lower and upper expected first passage and return times in imprecise birth-death chains. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 80, 137–173.
Vancouver
1.
Lopatatzidis S, De Bock J, De Cooman G. Computing lower and upper expected first passage and return times in imprecise birth-death chains. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. 2017;80:137–73.
MLA
Lopatatzidis, Stavros, Jasper De Bock, and Gert De Cooman. “Computing Lower and Upper Expected First Passage and Return Times in Imprecise Birth-death Chains.” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 80 (2017): 137–173. Print.