LEADER 02425nam 2200469 450 001 9910795262703321 005 20200106153738.0 010 $a1-4704-5416-5 035 $a(CKB)4940000000160189 035 $a(MiAaPQ)EBC5990834 035 $a(RPAM)21568215 035 $a(PPN)242520138 035 $a(EXLCZ)994940000000160189 100 $a20200106h20192019 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aTime-like graphical models /$fTvrtko Tadic? 210 1$aProvidence, RI :$cAmerican Mathematical Society,$d[2019] 210 4$dİ2019 215 $a1 online resource (184 pages) $ccolor illustrations 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vSeptember 2019, volume 261, number 1262 311 $a1-4704-3685-X 320 $aIncludes bibliographical references and index. 330 $a"We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs with an embedded time structure - so called time-like graphs. We extend the notion of time-like graphs and find properties of processes indexed by them. In particular, we solve the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. We provide a new result showing the stochastic heat equation as a limit of the sequence of natural Brownian motions on time-like graphs. In addition, our treatment of time-like graphical models reveals connections to Markov random fields, martingales indexed by directed sets and branching Markov processes"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vvol. 261, no. 1262. 606 $aGraphical modeling (Statistics) 606 $aMathematical statistics$xGraphic methods 615 0$aGraphical modeling (Statistics) 615 0$aMathematical statistics$xGraphic methods. 676 $a519.2/3 686 $a60G20$a60G60$a60H15$a60J65$a60J80$a62H05$a05C99$2msc 700 $aTadic?$b Tvrtko$01502100 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910795262703321 996 $aTime-like graphical models$93729637 997 $aUNINA