In this paper, we define and study a new class of random fields called harmonizable multi-operator scaling stable random fields. These fields satisfy a local asymptotic operator scaling property which generalizes both the local asymptotic self-similarity property and the operator scaling...

Bounds on the norming operators for distributions in the domain of semi-stable attraction of an operator semi-stable distribution are found. These bounds are used to establish the existence and nonexistence of moments of distributions in the domain of semi-stable attraction of an operator...

Coupled continuous time random walks (CTRWs) model normal and anomalous diffusion of random walkers by taking the sum of random jump lengths dependent on the random waiting times immediately preceding each jump. They are used to simulate diffusion-like processes in econophysics such as stock...

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return...

A sequence of independent, identically distributed random vectors X1, X2, X3,... is said to belong to the domain of attraction of a random vector Y is there exist linear operators An and constant vectors bn such that An(X1,..., Xn)+bn converges in distribution to Y. We present a simple,...

The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the underlying noise sequence has infinite fourth moment but finite second moment. In...

We introduce a bivariate distribution supported on the first quadrant with exponential, and heavy tailed Mittag-Leffer, marginal distributions. Although this distribution belongs to the class of geometric operator stable laws, it is a rather special case that does not follow their general...