The probabilistic Feynman-Kac formula for an infinite-dimensional Schrödinger equation with exponential and singular potentials

DOI10.1023/A:1008601707361zbMath0940.35207OpenAlexW221007366MaRDI QIDQ1304707

O. G. Smolyanov, Sergio A. Albeverio, Andrei Yu. Khrennikov

Publication date: 22 September 1999

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1008601707361

zbMATH Keywords

Schrödinger equationFeynman-Kac formulaabstract Wiener spaceinfinite-dimensional analysis

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Applications of stochastic analysis (to PDEs, etc.) (60H30) PDEs in connection with quantum mechanics (35Q40) Applications of manifolds of mappings to the sciences (58D30) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

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A global solution to the Schrödinger equation: From Henstock to Feynman ⋮ Feynman formula for Schrödinger-type equations with time- and space-dependent coefficients ⋮ Asymptotic expansions for ornstein-uhlenbeck semigroups perturbed by potentials over banach spaces ⋮ The Doss trick on symmetric spaces ⋮ Stochastic solutions of generalized time-fractional evolution equations

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