Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions

Sergio Albeverio, Hiroshi Kawabi, Michael Röckner

研究成果: Article査読

13 被引用数 (Scopus)

抄録

We prove Lp-uniqueness of Dirichlet operators for Gibbs measures on the path space C(R,Rd) associated with exponential type interactions in infinite volume by extending an SPDE approach presented in previous work by the last two named authors. We also give an SPDE characterization of the corresponding dynamics. In particular, for the first time, we prove existence and uniqueness of a strong solution for the SPDE, though the self-interaction potential is not assumed to be differentiable, hence the drift is possibly discontinuous. As examples, to which our results apply, we mention the stochastic quantization of P(φ)1-, exp(φ)1-, and trigonometric quantum fields in infinite volume. In particular, our results imply essential self-adjointness of the generator of the stochastic dynamics for these models. Finally, as an application of the strong uniqueness result for the SPDE, we prove some functional inequalities for diffusion semigroups generated by the above Dirichlet operators.

本文言語English
ページ(範囲)602-638
ページ数37
ジャーナルJournal of Functional Analysis
262
2
DOI
出版ステータスPublished - 2012 1月 15
外部発表はい

ASJC Scopus subject areas

  • 分析

フィンガープリント

「Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル