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Probabilistic Approximation of the Evolution Operator e –itH where \(H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}\)

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Abstract

Two approaches are suggested for constructing a probabilistic approximation of the evolution operator e–itH, where \(H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}\), in the strong operator topology. In the first approach, the approximating operators have the form of expectations of functionals of a certain Poisson point field, while, in the second approach, the approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables with finite moments of order 2m + 2.

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ACKNOWLEDGMENTS

We are grateful to N.V. Smorodina for her interest in this work and helpful comments.

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Authors and Affiliations

  1. St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences, 191023, St. Petersburg, Russia

    M. V. Platonova & S. V. Tcykin

  2. St. Petersburg State University, 199034, St. Petersburg, Russia

    M. V. Platonova

Authors
  1. M. V. Platonova
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  2. S. V. Tcykin
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Corresponding authors

Correspondence to M. V. Platonova or S. V. Tcykin.

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Translated by I. Ruzanova

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Platonova, M.V., Tcykin, S.V. Probabilistic Approximation of the Evolution Operator e –itH where \(H = \tfrac{{{{{( - 1)}}^{m}}}}{{(2m)!}}\tfrac{{{{d}^{{2m}}}}}{{d{{x}^{{2m}}}}}\) . Dokl. Math. 101, 144–146 (2020). https://doi.org/10.1134/S1064562420020192

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  • DOI: https://doi.org/10.1134/S1064562420020192

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