02425nam 2200469 450 991081063760332120200106153738.01-4704-5416-5(CKB)4940000000160189(MiAaPQ)EBC5990834(RPAM)21568215(PPN)242520138(EXLCZ)99494000000016018920200106h20192019 uy| 0engurcnu||||||||rdacontentrdamediardacarrierTime-like graphical models /Tvrtko TadićProvidence, RI :American Mathematical Society,[2019]©20191 online resource (184 pages) color illustrationsMemoirs of the American Mathematical Society,0065-9266 ;September 2019, volume 261, number 12621-4704-3685-X Includes bibliographical references and index."We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs with an embedded time structure - so called time-like graphs. We extend the notion of time-like graphs and find properties of processes indexed by them. In particular, we solve the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. We provide a new result showing the stochastic heat equation as a limit of the sequence of natural Brownian motions on time-like graphs. In addition, our treatment of time-like graphical models reveals connections to Markov random fields, martingales indexed by directed sets and branching Markov processes"--Provided by publisher.Memoirs of the American Mathematical Society ;vol. 261, no. 1262.Graphical modeling (Statistics)Mathematical statisticsGraphic methodsGraphical modeling (Statistics)Mathematical statisticsGraphic methods.519.2/360G2060G6060H1560J6560J8062H0505C99mscTadić Tvrtko1696945MiAaPQMiAaPQMiAaPQBOOK9910810637603321Time-like graphical models4077285UNINA