A REPRESENTATION OF EXCESSIVE FUNCTIONS AS EXPECTED
Abstract: For a nice Markov process such as Brownian motion on a domain in we prove
a representation of excessive functions in terms of expected suprema. This is motivated
by recent work of El Karoui  and El Karoui and Meziou  on the max-plus
decomposition for supermartingales. Our results provide a singular analogue to the
non-linear Riesz representation in El Karoui and Föllmer , and they extend the
representation of potentials in Föllmer and Knispel  by clarifying the role of the
boundary behavior and of the harmonic points of the given excessive function.
2000 AMS Mathematics Subject Classification: 60J45, 60J25, 31C05.
Key words and phrases: Markov processes, excessive functions, expected suprema.