Lattice approximation to the dynamical $\phi_{3}^{4}$ model

Zhu R, Zhu X (2018)
The Annals of Probability 46(1): 397-455.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We study the lattice approximations to the dynamical Phi(4)(3) model by paracontrolled distributions proposed in [Forum Math. Pi 3 (2015) e6]. We prove that the solutions to the lattice systems converge to the solution to the dynamical Phi(4)(3) model in probability, locally uniformly in time. Since the dynamical Phi(4)(3) model is not well defined in the classical sense and renormalisation has to be performed in order to define the nonlinear term, a corresponding suitable drift term is added in the stochastic equations for the lattice systems.
Stichworte
Phi(4)(3) model; regularity structure; paracontrolled distribution; space-time white noise; renormalisation
Erscheinungsjahr
2018
Zeitschriftentitel
The Annals of Probability
Band
46
Ausgabe
1
Seite(n)
397-455
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2920359

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Zhu R, Zhu X. Lattice approximation to the dynamical $\phi_{3}^{4}$ model. The Annals of Probability. 2018;46(1):397-455.
Zhu, R., & Zhu, X. (2018). Lattice approximation to the dynamical $\phi_{3}^{4}$ model. The Annals of Probability, 46(1), 397-455. doi:10.1214/17-AOP1188
Zhu, R., and Zhu, X. (2018). Lattice approximation to the dynamical $\phi_{3}^{4}$ model. The Annals of Probability 46, 397-455.
Zhu, R., & Zhu, X., 2018. Lattice approximation to the dynamical $\phi_{3}^{4}$ model. The Annals of Probability, 46(1), p 397-455.
R. Zhu and X. Zhu, “Lattice approximation to the dynamical $\phi_{3}^{4}$ model”, The Annals of Probability, vol. 46, 2018, pp. 397-455.
Zhu, R., Zhu, X.: Lattice approximation to the dynamical $\phi_{3}^{4}$ model. The Annals of Probability. 46, 397-455 (2018).
Zhu, Rongchan, and Zhu, Xiangchan. “Lattice approximation to the dynamical $\phi_{3}^{4}$ model”. The Annals of Probability 46.1 (2018): 397-455.