Some remarks on the martingales satisfying the structure equation
Tsung Ming Chao, Ching Sung Chou (2001)
Séminaire de probabilités de Strasbourg
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Some remarks on the martingales satisfying the structure equation
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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...