Geodesic
Probabilistic approximation of the Schr\"odinger equation by complex-valued random processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 17-28

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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. 
@article{ZNSL_2023_526_a1,
     author = {I. A. Alexeev and M. V. Platonova},
     title = {Probabilistic approximation of the {Schr\"odinger} equation by complex-valued random processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {17--28},
     publisher = {mathdoc},
     volume = {526},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a1/}
}
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I. A. Alexeev; M. V. Platonova. Probabilistic approximation of the Schr\"odinger 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/