Identification of the parameters of stable linear dynamical systems is a
well-studied problem in the literature, both in the low and high-dimensional
settings. However, there are hardly any results for the unstable case,
especially regarding finite time bounds. For this setting, classical results on
least-squares estimation of the dynamics parameters are not applicable and
therefore new concepts and technical approaches need to be developed to address
the issue. Unstable linear systems arise in key real applications in control
theory, econometrics, and finance. This study establishes finite time bounds
for the identification error of the least-squares estimates for a fairly large
class of heavy-tailed noise distributions, and transition matrices of such
systems. The results relate the time length (samples) required for estimation
to a function of the problem dimension and key characteristics of the true
underlying transition matrix and the noise distribution. To establish them,
appropriate concentration inequalities for random matrices and for sequences of
martingale differences are leveraged.

该研究针对不稳定线性系统的参数识别问题进行了研究，建立了针对重尾噪声分布和转移矩阵的一类较大误差最小二乘估计的有限时间界限，并与问题维度和真实转移矩阵的关键特征及噪声分布函数的性质相关联，并使用随机矩阵和鞅差序列的适当浓度不等式来实现这些结果。