We construct analogs of symmetric α-stable distributions for noninteger indices α > 2 and study their relations to solutions of the Cauchy problem for some evolution equations.
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I. A. Ibragimov, N. V. Smorodina, and M. M. Faddeev, “Complex analog of the central limit theorem and the probabilistic approximation of the Feynmann integral,” Dokl. Ros. Akad. Nauk, 459, 400–402 (2012).
T. Kato, Perturbation Theory for Linear Operators [Russian translation], Moscow (1972).
J. F. S. Kingman, Poisson Processes [Russian translation], Moscow (2007).
P. Koosis, Introduction to the Hp Spaces [Russian translation], Moscow (1984).
A. Lachal, “From pseudo-random walk to pseudo-Brownian motion: first exit time from a one-sided or a two-sided interval,” arXiv:1301.6579.
E. Orsingher and B. Toaldo, “Pseudoprocesses related to space-fractional higher-order heattype equations,” Stochast. Anal. Appl., 32, 619–641 (2014).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications [in Russian], Minsk (1997).
N. V. Smorodina and M. M. Faddeev, “Theorems on convergence of distributions of stochastic integrals to signed measures and local limit theorems for large deviations,” Zap. Nauchn. Semin. POMI, 368, 201–228 (2009).
N. V. Smorodina and M. M. Faddeev, “The L´evy–Khinchin representation of one class of signed stable measures and some its applications,” Acta Appl. Math., 110, 1289–1308 (2010).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 442, 2015, pp. 101–117.
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Platonova, M.V. Symmetric α-Stable Distributions with Noninteger α > 2 and Related Stochastic Processes. J Math Sci 225, 791–801 (2017). https://doi.org/10.1007/s10958-017-3494-1
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DOI: https://doi.org/10.1007/s10958-017-3494-1