Tauberian theory is concerned with the asymptotic properties of integral transforms. One Tauberian theorem, as shown by Feller (1971, chap. ⅩⅢ), states that a function is regularly varying at infinity if its Laplace transform regularly varying at zero. Many applications of limit theorems involving regular-varying functions arise in probability. The limit theorems are often proved by Laplace transforms using a Tauberian theorem. In Probabilistic Applications of Tauberian Theorems, Yakimiv develops multivariate versions of Tauberian theorems for regular varying functions and gives four applications of the results to probability theory.
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