On non-continuous Dirichlet processes

François Coquet (1) , Jean Mémin (1) , Leszek Slominski (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Faculty of Mathematics and Computer Science [Toruń]

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C 1 transformation.

Mots clés: Non-continuous Dirichlet process; stochastic integral; Itô formula

Domaines: Probabilités [math.PR]

François Coquet, Jean Mémin, Leszek Slominski. On non-continuous Dirichlet processes. Journal of Theoretical Probability, 2003, 16 (1), pp.197-216. ⟨10.1023/A:1022238723289⟩. ⟨hal-00725007⟩