ABSTRACT
The coordinate process {Xn : n = 0,1, • • • } defined on (S°°, <S0O°) by Xn(x) = xn (x = (xo, xi , • • • , xn , • • • )) is a MarJcovprocess with transition probability p(x, dy) and initial distribution ¡i. In other words, the conditional distribution of the process X+ := (Xn, Xn+i, • • • ) on (S°°, S®00) given ^ := ^{Xj : 0 < j < n}, namely the cr-field of past and present events up to time n, is Pxn, where Py is written for P^ with \i = Sy, i.e., /¿({y}) = 1. Often one needs a larger probability space than this canonical model (S°°, S®°°, PM) e.g., to accommodate a family of random variables independent of the process {Xn : n = 0,1, 2, • • • }.
