Abstract
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.
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Chen, M.F. Ergodic theorems for reaction-diffusion processes. J Stat Phys 58, 939–966 (1990). https://doi.org/10.1007/BF01026558
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DOI: https://doi.org/10.1007/BF01026558