Countably many simultaneous random changes of time scales (Q790544)

In this work the author extends previous work by himself [Adv. Math. 12, 32-57 (1974; Zbl 0379.60096)] on the finite dimensional-time changes case to the countably-infinite-dimensional time changes problem. For that he constructs the relevant processes, \(\sigma\)-algebras and defines correspondingly the infinitely many components time changes. He then proves, when the components are Feller processes, that the time changed process has the strong Markov-property (theorems 11 and 12) and extends Dynkin's lemma (theorem 13), but only for a restricted class of functions, namely functions that are finite products of one-variable functions. Besides the applications of the finitely many dimensional case in the author's previous paper, the reader can also check with \textit{T. G. Kurtz}'s paper in Ann. Probab. 8, 682-715 (1980; Zbl 0442.60072).