论文标题
非平稳马尔可夫矩阵产物的指数增长
Exponential growth of products of non-stationary Markov-dependent matrices
论文作者
论文摘要
Let $(ξ_j)_{j\ge1} $, be a non-stationary Markov chain with phase space $X$ and let $\mathfrak{g}_j:\,X\mapsto\mathrm{SL}(m,\mathbb{R})$ be a sequence of functions on $X$ with values in the unimodular group.设置$ g_j = \ mathfrak {g} _j（ξ_j）$，用$ s_n = g_n \ ldots g_1 $表示，矩阵$ g_j $的产物。当马尔可夫链不应该是固定的时，我们提供了足够的条件，以实现$ \ | s_n \ | $的指数增长。这概括了Furstenberg的经典定理，该定理在独立分布的矩阵的产品的指数增长以及Virtser扩展到固定的Markov依赖性矩阵的产品上。
Let $(ξ_j)_{j\ge1} $, be a non-stationary Markov chain with phase space $X$ and let $\mathfrak{g}_j:\,X\mapsto\mathrm{SL}(m,\mathbb{R})$ be a sequence of functions on $X$ with values in the unimodular group. Set $g_j=\mathfrak{g}_j(ξ_j)$ and denote by $S_n=g_n\ldots g_1$, the product of the matrices $g_j$. We provide sufficient conditions for exponential growth of the norm $\|S_n\|$ when the Markov chain is not supposed to be stationary. This generalizes the classical theorem of Furstenberg on the exponential growth of products of independent identically distributed matrices as well as its extension by Virtser to products of stationary Markov-dependent matrices.
