Geodesic
Nonprobabilistic analogues of the Cauchy process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 183-194 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is known that a solution of the Cauchy problem for an evolution equation having a convolution operator with a generalized function $|x|^{-2}$, in the right-hand side admits a probabilistic representation in the form of the expectation of a trajectory functional of the Cauchy process. We construct similar representations for evolution equations having a convolution operator with a generalized function $(-1)^m|x|^{-2m-2}$ for arbitrary $m\in\mathbf{N}$. 
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     author = {A. K. Nikolaev and M. V. Platonova},
     title = {Nonprobabilistic analogues of the {Cauchy} process},
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A. K. Nikolaev; M. V. Platonova. Nonprobabilistic analogues of the Cauchy process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 183-194. http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a12/

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