Geodesic
Approximation of the evolution operator by expectations of
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 17-35

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A method of probabilistic approximation of the operator $e^{-itH}$, where $H = -\frac{1}{2}\,\frac{d^2}{dx^2}+V(x)$, $V\in L_\infty(\mathbf R)$, in the strong operator topology is proposed. The approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables.
Mots-clés : evolution equations, Feynman–Kac formula.
Keywords: limit theorems 
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     author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
     title = {Approximation of the evolution operator by expectations of},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     volume = {64},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_1_a1/}
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. Approximation of the evolution operator by expectations of. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 17-35. http://geodesic.mathdoc.fr/item/TVP_2019_64_1_a1/