Jumps of the Canonical Process Associated with a Ray Semigroup

#### V. Grecea

2012, v.18, №2, 333-340

ABSTRACT

Given a (submarkovian) Ray semigroup ($P_t$) on a locally compact metric space $E$, we consider under some additional hypotheses the nonlocal part of the generator of ($P_t$), given by a kernel $l(x,\cdot)$, and we establish a relation between $l(x,\cdot)$ and the point process of the jumps of the canonical Ray process with "transition" semigroup ($P_t$).

Keywords: Ray semigroup,nonbranching point,Markov process,left limit,stopping time