0494316 20240103220618.020181009235959.9 85054396065 000446278400001 10.1007/s11040-018-9288-y 19 s. P cav_un_epca*02583621385-017221Springer Recursive tree process endogeny cav_un_auth*0365236 Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics 34 Mach Tibor UTIA-B CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0244526 Sturm A. DE cav_un_auth*0217893 Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics 33 Swart Jan M. UTIA-B CZ K Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2018/SI/swart-0494316.pdf cav_un_auth*0334217 GA16-15238S GA ČR CZ Aldous and Bandyopadhyay have shown that each solution to a recursive distributional equation (RDE) gives rise to a recursive tree process (RTP), which is a sort of Markov chain in which time has a tree-like structure and in which the state of each vertex is a random function of its descendants. If the state at the root is measurable with respect to the sigma field generated by the random functions attached to all vertices, then the RTP is said to be endogenous. For RTPs defined by continuous maps, Aldous and Bandyopadhyay showed that endogeny is equivalent to bivariate uniqueness, and they asked if the continuity hypothesis can be removed. We introduce a higher-level RDE that through its n-th moment measures contains all n-variate RDEs. We show that this higher-level RDE has minimal and maximal fixed points with respect to the convex order, and that these coincide if and only if the corresponding RTP is endogenous. As a side result, this allows us to answer the question of Aldous and Bandyopadhyay positively. WOS BA 10000 10100 10101 2019 3 4 A hod 4ah 20231122143440.8 RVO:67985556 http://hdl.handle.net/11104/0288959 1 1 Department of Stochastic Informatics UTIA-B 10103 STATISTICS & PROBABILITY S 30 2 Article Mathematics Applied|Physics Mathematical MATHEMATICS.APPLIED|PHYSICS.MATHEMATICAL 1.015 0.091 5.6 0.00137 0.776 264 0.781 1.054 33 Q3 62.101 46.1 Q2 Q2 0.62 Q3 49.409 2018 Soubory v repozitáři: swart-0494316.pdf 85054396065 SCOPUS PUBMED 000446278400001 WOS cav_un_epca*0258362 Mathematical Physics, Analysis and Geometry 1385-0172 1572-9656 Roč. 21 č. 4 2018 Springer