Stable distributions

By Svante Janson. 2011

210 citations recorded by the source corpus.

We give some explicit calculations for stable distributions and convergence to them, mainly based on less explicit results in Feller (1971). The main purpose is to provide ourselves with easy reference to explicit formulas and examples. (There are probably no new results.)

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/859b1520d648cf5c6f93afed8407372bb9e8901f

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In Mathematical Physics

Citations in the corpus

Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics (2020, background): “where Q(p) is the theoretical quantile of probability p for a Sα(γ, β, μ) variable [62, 2, 15].”
Pan-private algorithms via statistics on sketches (2011, methodology): “What is surprising is that without the constraints of pan-privacy, this approach yields approximations for higher frequency moments Fk = ∑ i a k i for k = 1 and 2 [10], but while we are able to derive pan-private distinct counts (related to F0) using the same approach, it does not work for pan-priva”
Portfolio diversification and value at risk under thick-tailedness (2009, unknown): “As discussed in Borak et al. (2005) and references therein, while stable heavy-tailed distributions with 2 (1, 2) provide a good fit for returns on some financial indices and other variables, many asset returns have the tail index greater than 2 or exhibit semi-heavy tails with finite moments of…”
On Hurst exponent estimation under heavy-tailed distributions (2010, background): “For more details about stable distributions, we refer readers to (Zolotarev, 1986; Samorodnitsky and Taqqu, 1994; Borak et al., 2005).”
The Fast Johnson--Lindenstrauss Transform and Approximate Nearest Neighbors (2009, methodology): “Indyk and Motwani [29] and Kushilevitz, Ostrovsky, and Rabani [33] used low-dimensional embeddings to speed up approximate nearest neighbor searching.”
Machine Learning of Space-Fractional Differential Equations (2018, background): “This can be misleading because it is not clear for what arguments an α-stable distribution is converged to a power law, nor is the answer simple; it depends on the parameter α, and the density enters into a transitory power law decay with power > 2 before settling into the “true” power law decay wit”
Nonparametric Testing of Distributions—the Epps–Singleton Two-Sample Test using the Empirical Characteristic Function (2009, background): “The article closes with some short conclusions.”