Probabilistic Approximation of the Solution of the Cauchy Problem for the Higher-Order Schrödinger Equation

DOI10.1137/S0040585X97T990125zbMath1469.60218OpenAlexW3126586001MaRDI QIDQ5150156

Sergei V. Tsykin, Mariya V. Platonova

Publication date: 9 February 2021

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97t990125

zbMATH Keywords

Schrödinger equationlimit theoremsPoisson random measure

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (1)

Pseudoprocesses related to higher-order equations of vibrations of rods

Cites Work

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• Probabilistic approximation of solutions of the Cauchy problem for some evolution equations
• On a limit theorem related to probabilistic representation of solution to the Cauchy problem for the Schrödinger equation
• Global estimates of fundamental solutions for higher-order Schrödinger equations
• Probabilistic approximation of the evolution operator
• A probabilistic representation of the Cauchy problem solution for the multidimensional Schrödinger equation
• A probabilistic approximation of the Cauchy problem solution for the Schrödinger equation with a fractional derivative operator
• Higher order Schrödinger equations
• Higher-order Schrödinger and Hartree–Fock equations

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