A Probabilistic Approximation of the Cauchy Problem Solution for the Schrödinger Equation with a Fractional Derivative Operator.

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A Probabilistic Approximation of the Cauchy Problem Solution for the Schrödinger Equation with a Fractional Derivative Operator. / Platonova, M.V.

In: Journal of Mathematical Sciences , Vol. 244, No. 5, 2020, p. 874-884.

Research output: Contribution to journal › Article

BibTeX

@article{759d788ca7024c06bb21fb069a0baef8,

title = "A Probabilistic Approximation of the Cauchy Problem Solution for the Schr{\"o}dinger Equation with a Fractional Derivative Operator.",

abstract = "We construct two types of probabilistic approximations of the Cauchy problem solution for the nonstationary Schr{\"o}dinger equation with a symmetric fractional derivative of order α ∈ (1, 2) at the right-hand side. In the first case, we approximate the solution by mathematical expectation of point Poisson field functionals, and in the second case, we approximate the solution by mathematical expectation of functionals of sums of independent random variables having a power asymptotics of a tail distribution.",

author = "M.V. Platonova",

year = "2020",

language = "English",

volume = "244",

pages = "874--884",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - A Probabilistic Approximation of the Cauchy Problem Solution for the Schrödinger Equation with a Fractional Derivative Operator.

AU - Platonova, M.V.

PY - 2020

Y1 - 2020

N2 - We construct two types of probabilistic approximations of the Cauchy problem solution for the nonstationary Schrödinger equation with a symmetric fractional derivative of order α ∈ (1, 2) at the right-hand side. In the first case, we approximate the solution by mathematical expectation of point Poisson field functionals, and in the second case, we approximate the solution by mathematical expectation of functionals of sums of independent random variables having a power asymptotics of a tail distribution.

AB - We construct two types of probabilistic approximations of the Cauchy problem solution for the nonstationary Schrödinger equation with a symmetric fractional derivative of order α ∈ (1, 2) at the right-hand side. In the first case, we approximate the solution by mathematical expectation of point Poisson field functionals, and in the second case, we approximate the solution by mathematical expectation of functionals of sums of independent random variables having a power asymptotics of a tail distribution.

M3 - Article

VL - 244

SP - 874

EP - 884

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 78539697