Linear Prediction for Some Rosenblatt and Rosenblatt-Volterra Processes  

作　　者：DUNCAN Tyrone E. PASIK-DUNCAN Bozenna 

机构地区：[1]Department of Mathematics,University of Kansas,Lawrence KS 66045,USA

出　　处：《Journal of Systems Science & Complexity》2025年第1期21-26,共6页系统科学与复杂性学报(英文版)

基　　金：supported by AFOSR under Grant No.FA9550-12-1-0384.

摘　　要：Rosenblatt and Rosenblatt-Volterra processes are two families of stochastic processes that are described by double Wiener-Itô integrals with singular kernels.The Rosenblatt processes have exponential singular kernels and the Rosenblatt-Volterra processes have singular Volterra kernels for the Wiener-Itô integrals.Empirical evidence shows that for many control systems the assumption of Gaussian noise is not appropriate so Rosenblatt and Rosenblatt-Volterra processes are some generalizations of Gaussian processes that can provide natural alternatives to Gaussian probability laws.Furthermore,the results for Rosenblatt and Rosenblatt-Volterra processes are tractable for some applications.These results can be compared to prediction for Gaussian processes and Gauss-Volterra processes.

关 键 词：Linear prediction prediction for Rosenblatt processes Rosenblatt processes Rosenblatt-Volterra processes 

分 类 号：O211[理学—概率论与数理统计]