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Potentials of a Markov process are expected suprema

Hans FöllmerThomas Knispel — 2007

ESAIM: Probability and Statistics

Expected suprema of a function  observed along the paths of a nice Markov process define an excessive function, and in fact a potential if  vanishes at the boundary. Conversely, we show under mild regularity conditions that any potential admits a representation in terms of expected suprema. Moreover, we identify the maximal and the minimal representing function in terms of probabilistic potential theory. Our results are motivated by the work of El Karoui and Meziou (2006) on the max-plus decomposition...

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