Abstract
We consider an operator K˚ϕ = Lϕ−: <CDU(x), Dϕ> in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, U∈W 1,4(H, μ) and μ is the invariant measure associated with L. We show that K˚ is essentially self-adjoint in the space L 2(H, ν) where ν is the “Gibbs” measure ν(dx) = Z −:1 e −:2U(x) dx. An application to Stochastic quantization is given.
This is a preview of subscription content, access via your institution.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Da Prato, G., Tubaro, L. Self-adjointness of some infinite-dimensional elliptic operators and application to stochastic quantization. Probab Theory Relat Fields 118, 131–145 (2000). https://doi.org/10.1007/s004400000073
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s004400000073
Mathematics Subject Classification (2000)
- 47B25
- 60H15
- 81S20
Key words
- Essential self-adjointness
- Stochastic partial differential equations
- Stochastic quantization