Geodesic
On Gaussian self-similar random fields on a 2-adic plane
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2020), pp. 94-99

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The article describes a new type of Gaussian fields on a two-dimensional 2-adic space, invariant under the translation group and group of scaling transformations (self-similar random fields). Fields are characterized by quadratic characteristic functionals defined by homogeneous generalized functions on a 2-adic space. The properties of the proposed generalized homogeneous functions are investigated and the positive definiteness of the correlation functionals is proved.
Keywords: Gaussian field, $p$-adic space, scaling transformation, characteristic functional, homo-geneous generalized function. 
@article{IVM_2020_5_a9,
     author = {M. D. Missarov},
     title = {On {Gaussian} self-similar random fields on a 2-adic plane},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {94--99},
     publisher = {mathdoc},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_5_a9/}
}
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M. D. Missarov. On Gaussian self-similar random fields on a 2-adic plane. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2020), pp. 94-99. http://geodesic.mathdoc.fr/item/IVM_2020_5_a9/