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1 results

  • 2 - Strong Markov Consistency of Multivariate Markov Families and Processes

  • from Part One - Consistencies
  • Tomasz R. Bielecki, Illinois Institute of Technology, Jacek Jakubowski, Uniwersytet Warszawski, Poland, Mariusz Niewȩgłowski
  • Book:
    Structured Dependence between Stochastic Processes
    Published online:
    18 September 2020
    Print publication:
    27 August 2020, pp 7-37

  • Summary

    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.