Mathematics – Probability
Scientific paper
2012-03-05
Mathematics
Probability
Scientific paper
We give a new approach for multi-parameter IDT processes and the main example of this kind of processes is the L\'{e}vy's $\mathbb{R}^{M}$-parameter Brownian motion studied by P. L\'{e}vy $\cite{Levy}$, N. N. Chentsov $\cite{Chentsov}$ and H. P. Mckean Jr. $\cite{Mckean}$. This new approach turn out to be very interesting since it provide several extension of most properties of the one-parameter IDT processes invested by R. Mansuy $\cite{Mansuy}$, K. Es-sebaiy and Y. Ouknine $\cite{Ouknine}$, and in our previous work $\cite{Hakassou}$. For instance, we prove that $\mathbb{R}_{+}^{N}$-parameter L\'{e}vy processes introduced by O. E. Barndorff-Nielsen et al. $\cite{Barndorff}$, are IDT in our sense and we prove the inheritance of multi-parameter IDT property under time change when base processes are $\mathbb{R}_{+}^{N}$-parameter L\'{e}vy processes. In this paper too, we are going to study intensively the multi-parameter IDT in the sense of K. Es-sebaiy and Y. Ouknine $\cite{Ouknine}$, and then we shall do a comparison with our approach.
Hakassou Antoine
Ouknine Youssef
No associations
LandOfFree
On multiparameter IDT processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On multiparameter IDT processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On multiparameter IDT processes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-132950