Criterions of ν-similarity for the two-dimensional birth-death processes

In the paper we examine ν-similarity of birth-death processes in two-dimensional case. A necessary condition for two processes being similar by obtaining relations between their birth and death rates is derived. We analyze situation for ν-similar birth-death processes, what is a generalization of the previous results for similar birth-and-death processes. In our case birth and death rates of two ν-similar processes are state-dependent ones. Special case as possible genetic application is provided. We include illustrative examples to validate presented results.