Before revision: The aim of this paper is to build dependent stochastic processes using the notion of self-decomposability in order to model dependence across different markets and extend some recently proposed multivariate L\'evy models based on subordination . Consequently, we study the properties of such processes, derive closed form expressions for  characteristic function and linear correlation coefficient and develop Monte Carlo schemes for their simulation.
After revision: The aim of this paper is to build dependent stochastic processes using the notion of self-decomposability in order to model dependence across different markets and extend some recently proposed multivariate L\'evy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related markets after a certain stochastic time delay . Consequently, we study the properties of such processes, derive closed form expressions for characteristic function and linear correlation coefficient and develop Monte Carlo schemes for their simulation.