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Bibliography

Journal Article

Pathwise duals of monotone and additive Markov processes

Sturm A., Swart Jan M.

: Journal of Theoretical Probability vol.31, 2 (2018), p. 932-983

: GAP201/12/2613, GA ČR

: pathwise duality, monotone Markov process, additive Markov process, interacting particle system

: 10.1007/s10959-016-0721-5

: http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf

(eng): 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

: 10101

2019-01-07 08:39