arXiv subjects

Gianluca Cassese

Publications and source records attributed to Gianluca Cassese.

20 records · Page 2Linked to original sources

arXiv2008

Sure Wins, Separating Probabilities and the Representation of Linear Functionals

We discuss conditions under which a convex cone $\K\subset \R^Ω$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions

math.FA↗

arXiv2008

Finitely Additive Supermartingales

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenous probability measure.

math.PR↗