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Limit Theorems on Convergence to Generalized Cauchy Type Processes

We prove a limit theorem on convergence of mathematical expectations of functionals of sums of independent random variables to a Cauchy problem solution for an evolution equation \( \frac{\partial u}{\partial t}={\left(-1\right)}^m{\mathcal{A}}_{\mu }, \) where \( {\mathcal{A}}_m \) is a convolution operator with a generalized function |x|−2m − 2, m ∈ N.

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Correspondence to A. K. Nikolaev.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 214–228.

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Nikolaev, A.K., Platonova, M.V. Limit Theorems on Convergence to Generalized Cauchy Type Processes. J Math Sci 258, 883–893 (2021).

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