Pathwise duals of monotone and additive Markov processes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00465436" target="_blank" >RIV/67985556:_____/18:00465436 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10959-016-0721-5" target="_blank" >http://dx.doi.org/10.1007/s10959-016-0721-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10959-016-0721-5" target="_blank" >10.1007/s10959-016-0721-5</a>
Alternative languages
Result language
angličtina
Original language name
Pathwise duals of monotone and additive Markov processes
Original language description
This paper develops a systematic treatment of monotonicity-based pathwise dualities for Markov processes taking values in partially ordered sets. We show that every Markov process that takes values in a finite partially ordered set and whose generator can be represented in monotone maps has a pathwise dual process. In the special setting of attractive spin systems this has been discovered earlier by Gray. We show that the dual simplifies a lot when the state space is a lattice (in the order-theoretic meaning of the word) and all monotone maps satisfy an additivity condition. This leads to a unified treatment of several well-known dualities, including Siegmund's dual for processes with a totally ordered state space, duality of additive spin systems, and a duality due to Krone for the two-stage contact process, and allows for the construction of new dualities as well.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GAP201%2F12%2F2613" target="_blank" >GAP201/12/2613: Threshold phenomena in stochastic systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Theoretical Probability
ISSN
0894-9840
e-ISSN
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Volume of the periodical
31
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
52
Pages from-to
932-983
UT code for WoS article
000432743300012
EID of the result in the Scopus database
2-s2.0-84994716320