The Markov group conjecture, a long‐standing open problem in the theory of Markov processes with countable state space, asserts that a strongly continuous Markov semigroup $T={(T_t)}_{t\in [0,\infty )}$ on ${\ell }^1$ has bounded generator if the operator $T_1$ is bijective. Attempts to disprove the conjecture have often aimed at glueing together finite‐dimensional matrix semigroups of growing dimension — that is, it was tried to show that the Markov group conjecture is false even for Markov processes that decouple into (infinitely many) finite‐dimensional systems.

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关于解耦的马尔可夫群猜想

马尔可夫群猜想是具有可数状态空间的马尔可夫过程理论中一个长期存在的开放问题，它断言一个强连续的马尔可夫半群 $Ť={（{Ť}_{Ť}）}_{Ť\in [0，\infty ）}$ 上 ${\ell }^{\mathrm{1个}}$ 如果运算符已限制了生成器 ${Ť}_{\mathrm{1个}}$是双射的。试图反驳这一猜想的目的通常是将增长维数的有限维矩阵半群粘合在一起-也就是说，试图证明即使对于解耦成（无限多个）有限维系统的马尔可夫过程，马尔可夫群猜想也是错误的。 。