Quick search | Browse volumes | |

VI: 21, 215-232, LNM 258 (1972)

**WALSH, John B.**

Transition functions of Markov processes (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 points

Comment: 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 compactification

Nature: Original

Retrieve article from Numdam

Transition functions of Markov processes (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 points

Comment: 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 compactification

Nature: Original

Retrieve article from Numdam