Geodesic
Probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in $d$-hyperball
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 149-170
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We extend the construction of probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in d-hyperball first obtained in the works by I. Ibragimov, N. Smorodina and M. Faddeev to a multidimensional case. Further on, we show that in these representations the Wiener process could be replaced by a random walk approximation. The $L_2$-convergence rates are obtained. 
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     author = {P. N. Ievlev},
     title = {Probabilistic representations for initial-boundary value problem solutions to the non-stationary {Schr\"odinger} equation in $d$-hyperball},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--170},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a10/}
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P. N. Ievlev. Probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in $d$-hyperball. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 149-170. http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a10/

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