0465436 20240103212940.420161115235959.9 84994716320 000432743300012 10.1007/s10959-016-0721-5 52 s. P cav_un_epca*02540800894-9840312 (2018)932-983Springer pathwise duality monotone Markov process additive Markov process interacting particle system cav_un_auth*0244526 50 Sturm A. DE cav_un_auth*0217893 Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics 50 Swart Jan M. UTIA-B CZ Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf cav_un_auth*0291241 GAP201/12/2613 GA ČR 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. BA 10000 10100 10101 2019 2 4 A hod 4ah 20231122142020.9 RVO:67985556 http://hdl.handle.net/11104/0265402 1 Department of Stochastic Informatics UTIA-B 10103 STATISTICS & PROBABILITY S 2 Article Statistics Probability STATISTICS&PROBABILITY 0.806 0.294 10.6 0.00333 0.793 877 0.902 0.674 85 Q4 50.343 23.2 Q2 Q2 0.47 Q3 23.171 2018 Soubory v repozitáři: swart-0465436.pdf 84994716320 SCOPUS 000432743300012 WOS cav_un_epca*0254080 Journal of Theoretical Probability 0894-9840 1572-9230 Roč. 31 č. 2 2018 932 983 Springer