The strong Markov property for canonical Wiener processes

A noncommutative analog of the concept of Markov time is formulated, in association with a canonical Wiener process (P, Q) [4]. For such a Markov time T, the quantities P_T(t) = P(t + T) ? P(T), Q_T(t) = Q(t + T) ? Q(T) can be defined using spectral integrals with operator-valued integrands, and constitute a new canonical Wiener process (P_T, Q_T), which is independent of the analog of the σ-field of events generated by the process up to the Markov time.