Published online by Cambridge University Press: 18 September 2020
In this chapter the concept of strong Markov consistency for multivariate Markov families and for multivariate Markov processes is introduced and studied. Strong Markov consistency of a multivariate Markov family/process, if satisfied, provides for invariance of the Markov property under coordinate projections, a property that is important in various practical applications. We only consider conservative Markov processes and Markov families. In Section 2.1, we study the so-called strong Markov consistency for multivariate Markov families and multivariate Markov processes taking values in an arbitrary metric space. This study is geared towards formulating a general framework within which the strong Markov consistency can be conveniently analyzed. In Section 2.2, we specify our study of the strong Markov consistency to the case of multivariate Feller-Markov families taking values in Rn. The analysis is first carried in the time-inhomogeneous case, and then in the time homogeneous case where a more comprehensive study can be done.