Abstract:We develop an Itô calculus for functionals of the "time" spent by a path at arbitrary levels. A Markovian setting is recovered by lifting a process X with its flow of occupation measures O and call the pair (O, X) the occupied process. While the occupation measure erases the chronology of the path, we show that our framework still includes many relevant problems in stochastic analysis and financial mathematics. The study of occupied processes therefore strikes a middle ground between the path-independent case … Show more
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