Open AccessFeller chains and random functions
Author(s) -
Vytautas Kazakevičius
Publication year - 2015
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.a.2015.09
Subject(s) - mathematics , random function , random element , function (biology) , probability generating function , random variable , random compact set , continuous function (set theory) , statistical physics , discrete mathematics , moment generating function , statistics , physics , evolutionary biology , biology
We prove that each Feller transition probability is the one-dimensional distribution of some stochastically continuous random function. We also introduce the notion of a regular random function and show, on one hand, that every random function has a regular modification, and on the other hand, that the composition of independent regular stochastically continuous random functions is stochastically continuous as well.