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

Albeverio S, Kawabi H, Roeckner M (2012)
Journal of Functional Analysis 262(2): 602-638.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We prove L(P)-uniqueness of Dirichlet operators for Gibbs measures on the path space C(R, R(d)) 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(phi)(1)-, exp(phi)(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. (C) 2011 Elsevier Inc. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
Journal of Functional Analysis
Band
262
Zeitschriftennummer
2
Seite
602-638
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Albeverio S, Kawabi H, Roeckner M. Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions. Journal of Functional Analysis. 2012;262(2):602-638.
Albeverio, S., Kawabi, H., & Roeckner, M. (2012). Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions. Journal of Functional Analysis, 262(2), 602-638. doi:10.1016/j.jfa.2011.09.023
Albeverio, S., Kawabi, H., and Roeckner, M. (2012). Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions. Journal of Functional Analysis 262, 602-638.
Albeverio, S., Kawabi, H., & Roeckner, M., 2012. Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions. Journal of Functional Analysis, 262(2), p 602-638.
S. Albeverio, H. Kawabi, and M. Roeckner, “Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions”, Journal of Functional Analysis, vol. 262, 2012, pp. 602-638.
Albeverio, S., Kawabi, H., Roeckner, M.: Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions. Journal of Functional Analysis. 262, 602-638 (2012).
Albeverio, Sergio, Kawabi, Hiroshi, and Roeckner, Michael. “Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions”. Journal of Functional Analysis 262.2 (2012): 602-638.