Ergodic theorems for reaction diffusion processes (Q808113)

New sufficient conditions are given for the ergodicity of reaction- diffusion processes which improve the known results. In the main criterion, contrary to the previous ones, the pure birth rate of the reaction plays a critical role. To do this, a new but natural coupling is introduced. It is proved that this coupling is the best one in some sense. One of the main results says that the reaction-diffusion processes are ergodic for all large enough pure rates.