0598658 20250715145757.420240926235959.9 Praha Katedra pravděpodobnosti a matematické statistiky MFF UK 2024 138 s. P pathwise duality interacting particle systems monotone Markov process monoid module cav_un_auth*0450907 Latz Jan Niklas UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI NL Ústav teorie informace a automatizace AV ČR, v. v. i. https://library.utia.cas.cz/separaty/2024/SI/latz-0598658.pdf SVV 260701 GA UK CZ cav_un_auth*0473203 GA20-08468S GA ČR cav_un_auth*0397552 In the study of Markov processes, duality is an important tool used to prove various types of long-time behavior. Nowadays, there exist two predominant approaches to Markov process duality: the algebraic one and the pathwise one. This thesis utilizes the pathwise approach in order to identify new dualities of interacting particle systems and to present previously known dualities within a unified framework. Three classes of pathwise dualities are identified by equipping the state space of an interacting particle system with the additional structure of a monoid, a module over a semiring, and a partially ordered set, respectively. This additional structure then induces a pathwise duality for each interacting particle system that preserves this structure in the sense that its generator can be written using only structure-preserving local maps. BA 10000 10100 10103 2025 Ph.D. Katedra pravděpodobnosti a matematické statistiky MFF UK Praha 2024 24.9.2024 1 RVO:67985556 https://hdl.handle.net/11104/0356717 cav_un_auth*0300034 Karlova Universita v Praze CZ S 2024 2024 Praha Katedra pravděpodobnosti a matematické statistiky MFF UK