Abstract:
The Wiener--Hopf (WH) equation is a semi-infinite Toeplitz system of equations that has diverse applications. In practice, truncation of the system is inevitable to calculate the solution of the WH equation in a finite time. Baxter's inequality provides an L_1-bound for the approximation error between the WH solution and its finite-section solution. However, this inequality is only valid for symbols with short memory. In this talk, we derive the Baxter-type convergence results for a block Toeplitz system when the corresponding matrix-valued symbol has a long memory. A key ingredient is using a series expansion of the inverse of a finite-order Toeplitz matrix. Based on these results, we show the Baxter-type convergence for linear prediction problems for multivariate long memory stationary processes. If time permits, we will discuss the frequency domain interpretation our approaches. This is a joint work with Akihiko Inoue.
2022-12-19 16:00 ~ 2022-12-19 17:00
梁埈豪博士(中央研究院)
第三綜合大樓2F 201