[{"intvolume":" 46","date_updated":"2019-06-17T11:46:30Z","department":[{"_id":"10020"}],"abstract":[{"text":"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.","lang":"eng"}],"author":[{"last_name":"Zhu","full_name":"Zhu, Rongchan","first_name":"Rongchan","id":"29023469"},{"last_name":"Zhu","full_name":"Zhu, Xiangchan","first_name":"Xiangchan","id":"29023414"}],"quality_controlled":"1","publisher":"Inst Mathematical Statistics","status":"public","keyword":["Phi(4)(3) model","regularity structure","paracontrolled distribution","space-time white noise","renormalisation"],"citation":{"harvard1":"Zhu, R., & Zhu, X., 2018. Lattice approximation to the dynamical $\\phi_{3}^{4}$ model. *The Annals of Probability*, 46(1), p 397-455.","mla":"Zhu, Rongchan, and Zhu, Xiangchan. “Lattice approximation to the dynamical $\\phi_{3}^{4}$ model”. *The Annals of Probability* 46.1 (2018): 397-455.","dgps":"Zhu, R. & Zhu, X. (2018). Lattice approximation to the dynamical $\\phi_{3}^{4}$ model. *The Annals of Probability*, *46*(1), 397-455. Inst Mathematical Statistics. doi:10.1214/17-AOP1188.

","ama":"Zhu R, Zhu X. Lattice approximation to the dynamical $\\phi_{3}^{4}$ model. *The Annals of Probability*. 2018;46(1):397-455.","wels":"Zhu, R.; Zhu, X. (2018): Lattice approximation to the dynamical $\\phi_{3}^{4}$ model *The Annals of Probability*,46:(1): 397-455.","bio1":"Zhu R, Zhu X (2018)

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

The Annals of Probability 46(1): 397-455.","ieee":" R. Zhu and X. Zhu, “Lattice approximation to the dynamical $\\phi_{3}^{4}$ model”, *The Annals of Probability*, vol. 46, 2018, pp. 397-455.","apa_indent":"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

","angewandte-chemie":"R. Zhu, and X. Zhu, “Lattice approximation to the dynamical $\\phi_{3}^{4}$ model”, *The Annals of Probability*, **2018**, *46*, 397-455.","lncs":" Zhu, R., Zhu, X.: Lattice approximation to the dynamical $\\phi_{3}^{4}$ model. The Annals of Probability. 46, 397-455 (2018).","frontiers":"Zhu, R., and Zhu, X. (2018). Lattice approximation to the dynamical $\\phi_{3}^{4}$ model. *The Annals of Probability* 46, 397-455.","chicago":"Zhu, Rongchan, and Zhu, Xiangchan. 2018. “Lattice approximation to the dynamical $\\phi_{3}^{4}$ model”. *The Annals of Probability* 46 (1): 397-455.

","apa":"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","default":"Zhu R, Zhu X (2018)

*The Annals of Probability* 46(1): 397-455."},"publication_status":"published","user_id":"89573","external_id":{"isi":["000430921800009"]},"year":"2018","date_created":"2018-06-04T07:03:56Z","type":"journal_article","isi":1,"page":"397-455","article_type":"original","publication_identifier":{"issn":["0091-1798"]},"volume":46,"doi":"10.1214/17-AOP1188","issue":"1","_id":"2920359","language":[{"iso":"eng"}],"title":"Lattice approximation to the dynamical $\\phi_{3}^{4}$ model","publication":"The Annals of Probability"}]