We prove the existence of the persistence exponent $$-\log\lambda:=\lim_{n\to\infty}\frac{1}{n}\log \mathbb{P}_\mu(X_0\in S,\ldots,X_n\in S)$$ for a class of time homogeneous Markov chains $\{X_i\}_{i\geq 0}$ in a Polish space, where $S$ is a Borel measurable set and $\mu$ is the initial distribution. Focusing on the case of AR($p$) and MA($q$) processes with $p,q\in N$ and continuous innovation distribution, we study the existence of $\lambda$ and its continuity in the parameters, for $S=\mathbb{R}_{\geq 0}$. For AR processes with log-concave innovation distribution, we prove the strict monotonicity of $\lambda$. Finally, we compute new explicit exponents in several concrete examples.

翻译：我们证明波兰空间内存在美元(美元)和美元(美元)的持久性Exponent $(美元)和美元(美元)的原始发行。我们以美元(美元)的AR(美元)和MA(美元)的个案和持续的创新分配为重点,我们研究了美元(美元)的存在及其在参数中的连续性,以美元(美元)和美元(美元)的参数。对于带有日志组合创新分配的AR进程,我们证明了美元(美元)的严格单一性。最后,我们在若干具体例子中进行了新的明确引用。