ERGODIC-THEOREMS FOR REACTION-DIFFUSION PROCESSES

New sufficient conditions are given for the ergodicity of reaction-diffusion processes which improve both Neuhauser's recent result and the present author's previous result. 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 birth rates. © 1990 Plenum Publishing Corporation.