Stochastic Holomorphy.
Calcul d'Ito sans probabilités
Phase transition and Martin boundary
Stochastische Bewegungen und ihre ersten Integrale.
Local martingales and filtration shrinkage
A general theory is developed for the projection of martingale related processes onto smaller filtrations, to which they are not even adapted. Martingales, supermartingales, and semimartingales retain their nature, but the case of local martingales is more delicate, as illustrated by an explicit case study for the inverse Bessel process. This has implications for the concept of No Free Lunch with Vanishing Risk, in Finance.
Relative Densities of Semimartingales.
Anticipation cancelled by a Girsanov transformation : a paradox on Wiener space
Potentials of a Markov process are expected suprema
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...
Local martingales and filtration shrinkage
A general theory is developed for the projection of martingale related processes onto smaller filtrations, to which they are not even adapted. Martingales, supermartingales, and semimartingales retain their nature, but the case of local martingales is more delicate, as illustrated by an explicit case study for the inverse Bessel process. This has implications for the concept of No Free Lunch with Vanishing Risk, in Finance.
A non-linear Riesz respresentation in probabilistic potential theory
On weak brownian motions of arbitrary order
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