INTERSECTIONS AND SHIFT FUNCTIONS OF STRONG MARKOVRANDOM CLOSED SETS
Ilya S. Molchanov
Abstract: If and are independent subsets of the positive half-line, then the function
is said to be a shift function of with respect to In
the paper both sets and are supposed to be strong Markov (or regenerative). It is
shown that the shift function is a harmonic function with respect to the kernel determined by
the transition probabilities of the corresponding semi-linear forward recurrence processes.
Conditions for the uniqueness of such a harmonic function with given boundary values are
presented.