论文标题
估计响应函数的累积方法在时间不变的线性系统中
Cumulant methods in the estimation of response functions in time-invariant linear systems
论文作者
论文摘要
论文专门用于在估算脉冲响应函数的估算中的应用，用于连续不变的线性系统，包括内部噪声的系统。该工作的主要假设是脉冲响应函数的二阶集成。我们的研究涉及对固定高斯随机过程之间样品交叉相关图的累积分析。对于这些二阶统计的高阶累积物，积分表示发挥了重要作用。使用图公式，所有表示形式均简化为涉及核的循环产物的积分总和。在工作中，我们证明了对相应积分的零的收敛性。然后，由于高斯分布是由其累积物确定的独特分布，并且估计量的所有高阶累积物也趋于零，因此我们建立了积分型跨核电图估计量的渐近正态性。
Thesis is devoted to the application of cumulant analysis in the estimation of impulse response functions for continuous time-invariant linear systems, including systems with inner noises. The main assumption of the work is the second-order integration of the impulse response function. Our study deals with cumulant analysis of sample cross-correlograms between stationary Gaussian stochastic processes. An important role was played by integral representations for the higher-order cumulants of these second-order statistics. Using the diagram formula, all representations are reduced to the finite sums of integrals involving cyclic products of kernels. In the work we proved the convergence to zero of the corresponding integrals. Then, since the Gaussian distribution is uniquelly determined by its cumulants and also all higher-order cumulants of the estimators tend to zero, we establish the asymptotic normality of the integral-type cross-correlogram estimators.
