关于连续时间线性系的确定性和概率性李雅普诺夫指数之间的差距
On the gap between deterministic and probabilistic Lyapunov exponents for continuous-time linear systems
摘要：
考虑一个非自治的连续时间线性系，其中决定动态特性的时变矩阵是分段常数，并取多个值$A_1, \dotsc, A_N$。本文研究了矩阵集$\{A_1, \dotsc, A_N\}$的最大李雅普诺夫指数与模式为$A_1, \dotsc, A_N$的分段确定马尔可夫过程的最大李雅普诺夫指数相等的情形.在这项研究中的一个基本步骤是建立一个结果的独立利益，即任何序列的马尔可夫过程与矩阵$A_1,\dotsc, A_N$收敛，直到提取一个子序列，马尔可夫过程与一个合适的凸组合的这些矩阵。
英文摘要：
Consider a non-autonomous continuous-time linear system in which the time-dependent matrix determining the dynamics is piecewise constant and takes finitely many values $A_1, \dotsc, A_N$. This paper studies the equality cases between the maximal Lyapunov exponent associated with the set of matrices $\{A_1, \dotsc, A_N\}$, on the one hand, and the corresponding ones for piecewise deterministic Markov processes with modes $A_1, \dotsc, A_N$, on the other hand. A fundamental step in this study consists in establishing a result of independent interest, namely, that any sequence of Markov processes associated with the matrices $A_1,\dotsc, A_N$ converges, up to extracting a subsequence, to a Markov process associated with a suitable convex combination of those matrices.
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