Probabilistic approximation of the evolution operator
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Publication:1791747
DOI10.1007/s10688-018-0216-5OpenAlexW2829896780WikidataQ129547187 ScholiaQ129547187MaRDI QIDQ1791747
I. A. Ibragimov, M. M. Faddeev, Nataliya V. Smorodina
Publication date: 11 October 2018
Published in: Functional Analysis and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10688-018-0216-5
Random fields (60G60) Applications of stochastic analysis (to PDEs, etc.) (60H30) Groups and semigroups of linear operators (47D03) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items (5)
An Analogue of the Feynman--Kac Formula for a High-Order Operator ⋮ Approximation of the Evolution Operator by Expectations of Functionals of Sums of Independent Random Variables ⋮ Probabilistic Approximation of the Solution of the Cauchy Problem for the Higher-Order Schrödinger Equation ⋮ Probabilistic approximation of the evolution operator \(e^{-itH}\) where \(H = \frac{( - 1)^m}{(2m)!} \frac{d^{2m}}{dx^{2m}}\) ⋮ On one limit theorem related to the Cauchy problem solution for the Schrödinger equation with a fractional derivative operator of order \(\alpha \in \bigcup_{m=3}^{\infty}\left(m-1,m\right)\)
Cites Work
- Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques
- On a limit theorem related to probabilistic representation of solution to the Cauchy problem for the Schrödinger equation
- A probabilistic representation of solution to the Cauchy problem for evolution equation with differential operator of order greater than 2
- Nonsingular transformations of symmetric Lévy processes
- Probabilistic Representation of a Solution of the Cauchy Problem for Evolution Equations with Riemann--Liouville Operators
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