Geodesic
On a~limit theorem related to probabilistic representation of the Cauchy problem solution for the Schr\"odinger equation
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 158-175

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We suggest a new method of a probabilistic approximation of the Cauchy problem solution for the unperturbed Schrödinger equation by expectations of functionals of some random walk. In contrast to our previous papers we do not suppose the existence of exponential moment for each step of the random walk. 
@article{ZNSL_2016_454_a8,
     author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
     title = {On a~limit theorem related to  probabilistic representation of the {Cauchy} problem solution for the {Schr\"odinger} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {158--175},
     publisher = {mathdoc},
     volume = {454},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a8/}
}
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. On a~limit theorem related to  probabilistic representation of the Cauchy problem solution for the Schr\"odinger equation. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 158-175. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a8/