ASYMPTOTICALLY STABLE PROCESS AND APPLICATIONS

Abstract

We remark that some stationary processes do not verify $x_\infty|x_\infty$ is equal to its value. To do this, we propose a new definitions to differentiate it in which a process is asymptotically stable if it verifies this property. We also remark that all processes in all financial models have missed this property. Which leads us to reexamine the models and look the impact and importance of this property.