Probabilistic representations of the initial-boundary value problem solutions for the Schrödinger equation in a $d$-dimensional ball

Authors: Pavel Ievlev

Published in: Zap. Nauchn. Sem. POMI (2018)

Date: July 2025

Abstract

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.

Keywords

Schrödinger equation, Boundary value problem, Probabilistic representations of PDE solutions

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BibTeX

@article{author2024title,
  title={Paper Title},
  author={Author, Name and Co-author, Name},
  journal={Journal Name},
  year={2024},
  publisher={Publisher}
}