Pathwise duals of monotone and additive Markov processes

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Pathwise duals of monotone and additive Markov processes

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Pathwise duals of monotone and additive Markov processes

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GAP201%2F12%2F2613" target="_blank" >GAP201/12/2613: Prahové jevy pro stochastické systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Theoretical Probability

ISSN

0894-9840

e-ISSN

—

Svazek periodika

31

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

52

Strana od-do

932-983

Kód UT WoS článku

000432743300012

EID výsledku v databázi Scopus

2-s2.0-84994716320