On the rate of escape or approach to the origin of a random string (Q2078120)

This paper is devoted to the study of a stochastic heat equation with an additive white noise in dimension \(d\). The author extends upon a result by \textit{C. Mueller} and \textit{R. Tribe} [Electron. J. Probab. 7, Paper No. 10, 29 p. (2002; Zbl 1010.60059)] regarding \textit{T. Funaki}'s model of a random string [Nagoya Math. J. 89, 129--193 (1983; Zbl 0531.60095)]. More precisely, he examines the rate of escape of this model in dimensions \(d\geq 7\). He also provides a bound for the rate of the approach to the origin in dimension \(d=6\).