Mutually catalytic branching processes and voter processes with strength of opinion

Since the seminal work of Dawson and Perkins, mutually catalytic versions of superprocesses have been studied frequently. In this article we combine two approaches extending their ideas: the approach of adding correlations to the driving noise of the system is combined with the approach of obtaining new processes by letting the branching rate tend to infinity. The processes are considered on a countable site space. We introduce infinite rate symbiotic branching processes which surprisingly can be interpreted as generalized voter processes with additional strength of opinions. Since many of the arguments go along the lines of known proofs this article is written in the style of a review article.