STABLE PROCESSES, MIXING, AND DISTRIBUTIONAL PROPERTIES. I

In this article, we consider real-valued stable Levy processes ( S(t)(alpha,beta,gamma,delta))(t)>= 0, where alpha, beta, gamma, delta are, respectively, the stability, skewness, scale, and drift coeffcients. We introduce the notion of mixed stable processes ( M(t)(alpha,beta,gamma,delta))(t)>= 0 ( i. e., we allow the skewness, scale, and drift coeffcients to be random). Our mixing procedure gives a structure of conditionally Levy processes. This procedure permits us to show that the sum of independent stable processes can be expressed via a mixed stable process.