On a super-diffusive, nonlinear birth and death process

The explicit and fully analytic transient solution for the transition probability density associated with a nonlinear birth and death process on Z is constructed. The time-dependent variance is proportional to t+Bt2 (with B being a constant), thus exhibiting a super-diffusive behavior. The space continuous limit of this process is a well-known diffusion process with nonlinear drift for which the transition probability density is also known explicitly in a very simple way