Random walks and measures on Hilbert space that are invariant with respect to shifts and rotations

DOI10.1007/s10958-019-04438-zzbMath1426.28027OpenAlexW2966769114MaRDI QIDQ2331352

V. Zh. Sakbaev

Publication date: 29 October 2019

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-019-04438-z

zbMATH Keywords

Cauchy problemdiffusion equationrandom walkfinitely additive measureChernov theoreminvariant measure on a group

Mathematics Subject Classification ID

Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Schrödinger and Feynman-Kac semigroups (47D08)

Related Items

Extension of the generalized Lebesgue-Feynman-Smolyanov measure on a Hilbert space ⋮ Unitary representation of walks along random vector fields and the Kolmogorov-Fokker-Planck equation in a Hilbert space ⋮ Shift-invariant measures on Hilbert and related function spaces ⋮ Sobolev spaces of functions on a Hilbert space endowed with a translation-invariant measure and approximations of semigroups ⋮ Quantum systems with infinite-dimensional coordinate space and the Fourier transform ⋮ Lebesgue-Feynman measures on infinite dimensional spaces ⋮ Diffusion on a Hilbert space equipped with a shift- and rotation-invariant measure ⋮ Representation of solutions of the Cauchy problem for a one-dimensional Schrödinger equation with a smooth bounded potential by quasi-Feynman formulae

Cites Work

• Notion of blowup of the solution set of differential equations and averaging of random semigroups
• Quasi-Feynman formulas -- a method of obtaining the evolution operator for the Schrödinger equation
• Non-Gaussian Lagrangian Feynman-Kac formulas
• Gaussian measures in Banach spaces
• Averaging of random walks and shift-invariant measures on a Hilbert space
• On the law of large numbers for compositions of independent random semigroups
• Does there exist a Lebesgue measure in the infinite-dimensional space?
• Unbounded random operators and Feynman formulae
• Products of independent random operators
• "Lebesgue Measure" on R ∞
• One-Parameter Semigroups for Linear Evolution Equations
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