A contribution to the study of the IDT processes

Details A contribution to the study of the IDT processes A contribution to the study of the IDT processes

2012-03-05

arxiv.org/abs/1203.0874v1

Mathematics

Probability

Scientific paper

The notion of processes which are infinitely divisible with respect to time (in short IDT processes) has been introduced by R. Mansuy in 2005 like a wide generalization of L\'evy processes. Various properties of these processes have been already established in R. Mansuy. In 2007, the work of K. Es-sebaiy and Y. Ouknine $\cite{Ouknine}$ revealed more properties on this kind of processes. The purpose of this paper is to give several new examples of IDT processes for which we can explicit associated L\'evy processes. Each time, these examples were based on the sheet's concept like the L\'evy sheet (for which the Brownian sheet is a special case), the Gaussian sheet and the Sato sheet. In this paper, we also give a new concept of weak IDT processes, an integrated It\^o's type formula for IDT processes and a link between IDT processes and selfdecomposability.

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