AI 中文总结
研究相互催化超马尔可夫链的强唯一性问题，通过找到特定函数及方程并论证其唯一性，在不可约两态情况应用弱收敛方法建立大偏差原理。
AI 中文摘要
本文研究相互催化超马尔可夫链的强唯一性问题，它是一个具有赫尔德连续系数的二维退化随机微分方程。关键步骤是找到一个由两个耦合过程构成的函数且满足一维自治随机微分方程，通过Yamada-Watanabe论证得出该方程的唯一性。然后在不可约两态情况下，应用Budhiraja、Dupuis和Maroulas的弱收敛方法于控制方程建立大偏差原理。
英文摘要
In this paper, we study the strong uniqueness problem for the mutually catalytic super-Markov chain, which is a two-dimensional degenerate stochastic differential equation with Hölder continuous coefficients. The key step is to find a process which is a function of two coupled processes and satisfies an autonomous one-dimensional stochastic differential equation; uniqueness for this equation follows from a Yamada-Watanabe argument. A large deviation principle is then established, in the irreducible two-state case, by applying the weak-convergence approach of Budhiraja, Dupuis and Maroulas to the controlled equations.
