Duality Under a New Setting

Abstract

This is a continuation of [2]. The developments there are complicated by an exceptional set denoted by Z (see [2], p. 179). It is shown that Z is a polar set under the conditions there if and only if Hunt’s Hypothesis (B) holds (see [2], p, 192). In this paper a set of sufficcient conditions on the potential kernel will be given for the absence of Z. These strengthen the conditions used in [2]. The dual semigroup {P0302t, t ≥ 0} (see 2 , p. 191) is then defined on the state space E∂, some of its properties will be reviewed and adduced. A process will then be constructed with the dual semigroup as its transition semigroup, which will be shown to be a Hunt process on E∂. This process is in (strong) duality with the original Hunt Process in the sense of [1].