Advanced search
1 file | 879.17 KB

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

Stavros Lopatatzidis (UGent) , Jasper De Bock (UGent) and Gert De Cooman (UGent)
Author
Organization
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.
Keywords
Birth–death chain, First-passage time, Return time, Lower expectation, Imprecise probability, Submartingale

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 879.17 KB

Citation

Please use this url to cite or link to this publication:

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.
@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},
}

Altmetric
View in Altmetric