Geodesic
Symmetric $\alpha$-stable distributions for noninteger $\alpha>2$ and related stochastic processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 101-117

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We construct analogues of symmetric $\alpha$-stable distributions for noninteger indices $\alpha>2$ and investigate their links to solutions of the Cauchy problem for some evolution equations. 
@article{ZNSL_2015_442_a5,
     author = {M. V. Platonova},
     title = {Symmetric $\alpha$-stable distributions for noninteger $\alpha>2$ and related stochastic processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--117},
     publisher = {mathdoc},
     volume = {442},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a5/}
}
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M. V. Platonova. Symmetric $\alpha$-stable distributions for noninteger $\alpha>2$ and related stochastic processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 101-117. http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a5/