Transformation of state space for two-parameter Markov processes

Let X=(X(r)) be a two-parameter *-Markov process with a transition function (p(1), p(2), p), where X(r) takes values in the state space (E(r), E(r)), r is an element of T=[0, infinity)(2). For each r is an element of T, let f, be a measurable transformation of (E(r), E(4)) into the state space (E'(r), E(r)). Set Y-r=f(r)(X(r)), r is an element of T. A sufficient condition is given for the process Y=(Y-r) still to be a two-parameter *-Markov process with a transition function in terms of transition function (p(1), p(2), p) and f(r). For *-Markov families of two-parameter processes with a transition function, a similar problem is also discussed.