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: 21, 215-232, LNM 258 (1972)WALSH, John B.
Transition functions of Markov processes
Assume that a cadlag process satisfies the strong Markov property with respect to some family of kernels $P_t$ (not necessarily a semigroup). It is shown that these kernels can be modified into a true strong Markov transition function with a few additional properties. A similar problem is solved for a left continuous, moderate Markov process. The technique involves a Ray compactification which is eliminated at the end, and a useful lemma shows how to construct supermedian functions which separate pointsComment:
The problem discussed here has great theoretical importance, but little practical importance except for time reversal. The construction of a nice transition function for a Markov process has been also discussed by Kuznetsov ()Keywords: Transition functions
, Strong Markov property
, Moderate Markov property
, Ray compactificationNature: Original Retrieve article from Numdam