This work provides explicit conditions to establish the dimension-free Harnack inequalities respectively for state-independent and state-dependent regime-switching processes. Then such Harnack inequalities are applied to establish the hypercontractivity of the associated semigroup, and further to study the long time asymptotics of unbounded additive functionals of regime-switching processes. Much effort is devoted to overcoming the difficulty caused by the close interaction between the diffusion processes and the Markov chains in the setting of regime-switching processes.

中文翻译：

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区域转换扩散过程的无穷加性功能的Harnack不等式和长时间渐近性

这项工作为分别建立与状态无关和与状态有关的体制转换过程的无量纲哈纳克不等式提供了明确的条件。然后将此类Harnack不等式应用于建立关联半群的超收缩性，并进一步研究政权转换过程的无穷加性功能的长时间渐近性。为了克服由扩散过程和马尔可夫链之间在制度转换过程中的紧密相互作用所造成的困难，人们付出了很多努力。