A random field approach to weak convergence of processes
It is known that to a process with path in \(D([0,1],{\mathcal S}'( {\mathbf R}^ d))\) a space-time random field in \({\mathcal S}'({\mathbf R}^{d+1})\) can be associated [cf. the reviewer, the first author and \textit{S. Ramaswamy}, J. Funct. Anal. 66, 21-41 (1986; Zbl 0589.46027)]. The authors give conditions, formulated in terms of the space-time random fields only, which imply the weak convergence of the corresponding processes. For continuous limit these conditions are shown to be necessary. An example of application to investigate the fluctuation limit of an infinite particle system is given.
fluctuation limit of an infinite particle system
scientific article; zbMATH DE number 445283
scientific article