A remark on the connection between stochastic mechanics and the heat equation

DOI10.1063/1.1666536zbMath0291.60028OpenAlexW1985993008MaRDI QIDQ4042414

Raphael J. Høegh-Krohn, Sergio A. Albeverio

Publication date: 1974

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://urn.nb.no/URN:NBN:no-48401

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Heat equation (35K05) Schrödinger operator, Schrödinger equation (35J10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (max. 100)

To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space ⋮ Sharp estimates for capacities and applications to symmetric diffusions ⋮ Diffusion processes with singular drift fields ⋮ Transformations of diffusion and Schrödinger processes ⋮ A generalization of the Fenyes - Nelson stochastic model of quantum mechanics ⋮ Stochastic interpretation of Feynman path integral ⋮ Introducing randomness into first-order and second-order deterministic differential equations ⋮ Variational processes and stochastic versions of mechanics ⋮ Nelson-Brown motion: Some question marks ⋮ The Albeverio-Høegh-Krohn paradox in Nelson stochastic mechanics ⋮ Unnamed Item ⋮ Exact solutions of Fokker-Planck equations associated to quantum wave functions ⋮ Stochastic mechanics and the Feynman integral ⋮ Lévy flights and nonlocal quantum dynamics ⋮ Dirichlet forms and diffusion processes on rigged Hilbert spaces ⋮ Stochastic calculus of variations ⋮ Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation ⋮ Energy forms, Hamiltonians, and distorted Brownian paths ⋮ Homogeneous random fields and statistical mechanics ⋮ Stochastic fields from stochastic mechanics ⋮ Processus gaussiens, equivalence d'ensembles et specification locale ⋮ Regularization of Hamiltonians and processes ⋮ Conservative diffusions ⋮ Stochastic dynamics: A review of stochastic calculus of variations ⋮ Geometry of the Schrödinger equation and stochastic mass transportation ⋮ On a certain class of two-sided continuous local semimartingales: Toward a sample-wise characterization of the Nelson process ⋮ Malliavin calculus and Euclidean quantum mechanics. I: Functional calculus

This page was built for publication: A remark on the connection between stochastic mechanics and the heat equation