Applications of Revuz and Palm Type Measures for Additive Functionals in Weak Duality

Abstract

Several characterizations of additive functionals of a Markov process have been described in recent years. Under strong (Hunt) duality hypotheses this was accomplished in a series of papers by Revuz [14], [15], Getoor [9], and Sharpe [17]; for “symmetric” processes this was done by Fukushima [7] and Dynkin [4], [5]; earlier, the situation for Markov stochastic systems was investigated by Dynkin [3], [6]. Here, we obtain results along the same lines for processes in weak duality. The main tool is the “auxiliary process” [13] associated to a pair of Markov processes in weak duality. (Some facts about this process are recalled below.) Our approach is guided in part by similarities with the theory of flows ([8], [16]) and exploits the interplay between optionality and cooptionality in this context.