Geodesic
Probabilistic approximation of the Schrödinger equation by complex-valued random processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 17-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method for probabilistic approximation of the solution of the Cauchy problem for a one-dimensional unperturbed Schrödinger equation by mathematical expectations of functionals of some complex-valued Lévy process is proposed. In contrast to previous papers, we obtain the convergence rate of the constructed approximation to the exact solution for a wider class of initial functions. 
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     author = {I. A. Alexeev and M. V. Platonova},
     title = {Probabilistic approximation of the {Schr\"odinger} equation by complex-valued random processes},
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I. A. Alexeev; M. V. Platonova. Probabilistic approximation of the Schrödinger equation by complex-valued random processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 17-28. http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a1/

[1] I. A. Alekseev, “Ustoichivye sluchainye velichiny s kompleksnym indeksom ustoichivosti, II”, Teoriya veroyatn. i ee primen., 67:4 (2022), 627–648 | DOI

[2] I. A. Alekseev, “Veroyatnostnaya approksimatsiya operatora tipa Rimana–Liuvillya s indeksom ustoichivosti bolshe dvukh”, Zap. nauchn. semin. POMI, 510, 2022, 5–27

[3] I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Ob odnoi predelnoi teoreme, svyazannoi s veroyatnostnym predstavleniem resheniya zadachi Koshi s operatorom Shrëdingera”, Zap. nauchn. semin. POMI, 454, 2016, 158–175

[4] I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Veroyatnostnaya approksimatsiya operatora evolyutsii”, Funkts. analiz i ego pril., 52:2 (2018), 25–39 | DOI | MR

[5] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[6] Dzh. Kingman, Puassonovskie protsessy, MTsNMO, M., 2007

[7] M. V. Platonova, S. V. Tsykin, “Veroyatnostnaya approksimatsiya resheniya zadachi Koshi dlya uravneniya Shrëdingera vysokogo poryadka”, Teoriya veroyatn. i ee primen., 65:4 (2020), 710–724 | DOI | MR

[8] M. V. Platonova, “Analog formuly Feinmana–Katsa dlya operatora vysokogo poryadka”, Teoriya veroyatn. i ee primen., 67:1 (2022), 81–99 | DOI

[9] A. V. Skorokhod, Sluchainye protsessy s nezavisimymi prirascheniyami, Nauka, M., 1964