Applying monoid duality to a double contact process

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F23%3A00572568" target="_blank" >RIV/67985556:_____/23:00572568 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/23:10465394
Result on the web
<a href="https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Applying-monoid-duality-to-a-double-contact-process/10.1214/23-EJP961.full" target="_blank" >https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Applying-monoid-duality-to-a-double-contact-process/10.1214/23-EJP961.full</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/23-EJP961" target="_blank" >10.1214/23-EJP961</a>

Result language
angličtina
Original language name
Applying monoid duality to a double contact process
Original language description
In this paper we use duality techniques to study a coupling of the well-known contact process (CP) and the annihilating branching process. As the latter can be seen as a cancellative version of the contact process, we rebrand it as the cancellative contact process (cCP). Our process of interest will consist of two components, the first being a CP and the second being a cCP. We call this process the double contact process (2CP) and prove that it has (depending on the model parameters) at most one invariant law under which ones are present in both processes. In particular, we can choose the model parameters in such a way that CP and cCP are monotonely coupled. In this case also the above mentioned invariant law will have the property that, under it, ones (modeling “infected individuals”) can only be present in the cCP at sites where there are also ones in the CP. Along the way we extend the dualities for Markov processes discovered in our paper “Commutative monoid duality” to processes on infinite state spaces so that they, in particular, can be used for interacting particle systems.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA20-08468S" target="_blank" >GA20-08468S: Large scale limits of interacting stochastic models</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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