Long range dependence of heavy-tailed random functions

We introduce a definition of long range dependence of random processes and fields on an (unbounded) index space $T\subseteq \mathbb{R}^d$ in terms of integrability of the covariance of indicators that a random function exceeds any given level. This definition is specifically designed to cover the case of random functions with infinite variance. We show the value of this new definition and its connection to limit theorems via some examples including subordinated Gaussian as well as random volatility fields and time series.

Human Motion Data Retrieval Based on Staged Dynamic Time Deformation Optimization Algorithm

In recent years, with the rapid development of computer storage capabilities and network transmission capabilities, users can easily share their own video and image information on social networking sites, and the amount of multimedia data on the network is rapidly increasing. With the continuous increase of the amount of data in the network, the establishment of effective automated data management methods and search methods has become an increasingly urgent need. This paper proposes a retrieval method of human motion data based on motion capture in index space. By extracting key frames from the original motion to perform horizontal dimensionality reduction and defining features based on Laban motion analysis, the motion segment is subjected to vertical feature dimensionality reduction. After extracting features from the input motion segment, motion matching is performed on the index space. This paper designs the optimization method of the phased dynamic time deformation algorithm in time efficiency and analyzes the optimization method of the phased dynamic time deformation algorithm in time complexity. Considering the time efficiency redundancy, this paper optimizes the time complexity of the phased dynamic time deformation method. This improves the time efficiency of the staged dynamic time warping algorithm, making it suitable for larger-scale human motion data problems. Experiments show that the method in this paper has the advantage of speed, is more in line with the semantics of human motion, and can meet the retrieval requirements of human motion databases.

On generalized max-linear models in max-stable random fields

In practice, it is not possible to observe a whole max-stable random field. Therefore, we propose a method to reconstruct a max-stable random field in C([0, 1]k) by interpolating its realizations at finitely many points. The resulting interpolating process is again a max-stable random field. This approach uses a generalized max-linear model. Promising results have been established in the k = 1 case of Falk et al. (2015). However, the extension to higher dimensions is not straightforward since we lose the natural order of the index space.