Multivariate Regular Variation in Probability Theory

Local Limit Theorem for the Multiple Power Series Distributions

“…The definition of regularly varying multiple power series is given in [23]. A brief overview of various definitions of multivariate regularly varying functions is available in [27]. The history of different class functions having slow (one-sided or ordinary) oscillation can be seen in the book [24].…”

“…Timashev used the method of moments in his aforementioned result. In the papers [20,22,27] and in this article, we use the corresponding Tauberian statements. All these statements go back to Karamata's well-known Tauberian theorems [29,30].…”