Abstract
In this chapter we introduce the class of extended p-tempered α-stable distributions, which is the smallest class of models that contains TS α p and is closed under weak convergence. We then characterize weak convergence of sequences in this class.
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Notes
- 1.
A set A is said to be bounded away from 0 if 0 is not in the closure of A, i.e. \(0\notin \bar{A}\).
- 2.
Specifically, Propositions 3.16 and 3.17 in [62] imply that \(M(\bar{\mathbb{R}}^{d})\) is vaguely relatively compact and metrizable as a complete and separable metric space. From here the result follows from the fact that relative compactness and sequential relative compactness are equivalent in metrizable spaces, see, e.g., pages 4–5 in [13].
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© 2016 Michael Grabchak
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Grabchak, M. (2016). Limit Theorems for Tempered Stable Distributions. In: Tempered Stable Distributions. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-24927-8_4
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DOI: https://doi.org/10.1007/978-3-319-24927-8_4
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