论文标题
自回归随机序列的非标准极限
Non-standard limits for a family of autoregressive stochastic sequences
论文作者
论文摘要
我们考虑了一个多元自回归随机序列的家族，该序列在撞击原点附近时重新启动，并在自动回归系数趋向于一个时研究它们的分布限制，噪声缩放参数趋于零，并且邻域大小变化。我们获得了一个非标准极限定理，其中限制分布是原子分布的混合物和绝对连续的分布，其边缘又是正常随机变量的签名绝对值的分布的混合物。特别是，我们提供了使限制分布正常的条件，例如在没有重新启动机制的情况下。主要定理伴随着许多示例和辅助结果。
We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling parameter tends to zero, and the neighbourhood size varies. We obtain a non-standard limit theorem where the limiting distribution is a mixture of an atomic distribution and an absolutely continuous distribution whose marginals, in turn, are mixtures of distributions of signed absolute values of normal random variables. In particular, we provide conditions for the limiting distribution to be normal, like in the case without restart mechanism. The main theorem is accompanied by a number of examples and auxiliary results of their own interest.
