Geodesic
A method for solving the $p$-adic Kolmogorov–Feller equation for an ultrametric random walk in an axially symmetric external field
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 197-207
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A method for solving the Kolmogorov–Feller equation for an ultrametric random walk in an axially symmetric external field is considered. The transition function $w(y\mid x)$, $x,y\in\mathbb Q_p$, of the process under consideration is nonsymmetric and depends on the norm of $p$-adic arguments. It is proved for the transition functions of the form $w(y\mid x)=\rho(|x-y|_p)\varphi(|x|_p)$ that solving the $p$-adic Kolmogorov–Feller equation for a random walk in a $p$-adic ball of radius $p^R$ reduces to solving a system of $R+1$ ordinary differential equations. 
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     title = {A~method for solving the $p$-adic {Kolmogorov{\textendash}Feller} equation for an ultrametric random walk in an axially symmetric external field},
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O. M. Sizova. A method for solving the $p$-adic Kolmogorov–Feller equation for an ultrametric random walk in an axially symmetric external field. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 197-207. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a15/

[1] Avetisov V. A., Bikulov A. H., “Protein ultrametricity and spectral diffusion in deeply frozen proteins”, Biophys. Rev. Lett., 3 (2008), 387–396 | DOI

[2] Avetisov V. A., Bikulov A. H., Kozyrev S. V., “Application of $p$-adic analysis to models of spontaneous breaking of replica symmetry”, J. Phys. A, 32 (1999), 8785–8791 | DOI | MR | Zbl

[3] Avetisov V. A., Bikulov A. H., Kozyrev S. V., Osipov V. A., “$p$-adic models of ultrametric diffusionh constrained by hierarchical energy landscapes”, J. Phys. A: Math. Gen., 35 (2002), 177–189 | DOI | MR | Zbl

[4] Avetisov V. A., Bikulov A. H., Osipov V. A., “$p$-adic models of ultrametric diffusion in conformational dynamics of macromolecules”, Proc. Steklov Inst. Math., 245, 2004, 48–57 | MR | Zbl

[5] Frauenfelder H., “The connection between low-temperature kinetics and life”, Protein Structure, Molecular and Electronic Reactivity, eds. R. H. Austin et al., Springer, New York, 1987, 245–261 | DOI

[6] Morozov L., Tamm M. V., Nechaev S. K., Avetisov V. A., Statistical model of intra-chromosome contact maps, 2013, arXiv: 1311.7689

[7] Ogielski A. T., Stein D. L., “Dynamics on ultrametric spaces”, Phys. Rev. Lett., 55 (1985), 1634–1637 | DOI | MR

[8] Parisi G., “Infinite number of order parameters for spin-glasses”, Phys. Rev. Lett., 43 (1979), 1754–1756 | DOI | MR

[9] Rammal R., Toulose G., Virasoro M. A., “Ultrametrisity for physicists”, Rev. Mod. Phys., 58:3 (1986), 765–788 | DOI | MR