Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications

Röckner M, Zhu R, Zhu X (2017)
Journal of Functional Analysis 272(10): 4263-4303.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
In this paper we obtain restricted Markov uniqueness of the generator and uniqueness of martingale (probabilistically weak) solutions for the stochastic quantization problem in both the finite and infinite volume case by clarifying the precise relation between the solutions to the stochastic quantization problem obtained by the Dirichlet form approach and those obtained in [10] and in [24]. We prove that the solution X - Z, where X is obtained by the Dirichlet form approach in [4] and Z is the corresponding O-U process, satisfies the corresponding shifted equation (see (1.4) below). Moreover, we obtain that the infinite volume p(Phi)(2) quantum field is an invariant measure for the (K) over bar = Y Z, where Y is the unique solution to the shifted equation. (C) 2017 Elsevier Inc. All rights reserved.
Stichworte
Stochastic quantization problem; Dirichlet forms; Space-time white; noise; Wick power
Erscheinungsjahr
2017
Zeitschriftentitel
Journal of Functional Analysis
Band
272
Ausgabe
10
Seite(n)
4263-4303
ISSN
0022-1236
eISSN
1096-0783
Page URI
https://pub.uni-bielefeld.de/record/2911002

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Röckner M, Zhu R, Zhu X. Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications. Journal of Functional Analysis. 2017;272(10):4263-4303.
Röckner, M., Zhu, R., & Zhu, X. (2017). Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications. Journal of Functional Analysis, 272(10), 4263-4303. doi:10.1016/j.jfa.2017.01.023
Röckner, M., Zhu, R., and Zhu, X. (2017). Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications. Journal of Functional Analysis 272, 4263-4303.
Röckner, M., Zhu, R., & Zhu, X., 2017. Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications. Journal of Functional Analysis, 272(10), p 4263-4303.
M. Röckner, R. Zhu, and X. Zhu, “Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications”, Journal of Functional Analysis, vol. 272, 2017, pp. 4263-4303.
Röckner, M., Zhu, R., Zhu, X.: Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications. Journal of Functional Analysis. 272, 4263-4303 (2017).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “Restricted Markov uniqueness for the stochastic quantization of P(Phi)(2) and its applications”. Journal of Functional Analysis 272.10 (2017): 4263-4303.