Optimal Linear Filtering, Smoothing and Trend Extraction of M-Period Differences of Processes with a Unit Root

2008 ◽  
Author(s):  
Dimitrios D. Thomakos
Keyword(s):  
Unit Root ◽  
Linear Filtering ◽  
Trend Extraction ◽  
Optimal Linear ◽  
Optimal Linear Filtering

scholarly journals Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals

2001 ◽  
Vol 14 (3) ◽  
pp. 215-226 ◽  
Author(s):  
M. L. Kleptsyna ◽  
A. Le Breton
Keyword(s):  
Gaussian Processes ◽  
Laplace Transforms ◽  
Quadratic Functional ◽  
Linear Filtering ◽  
Volterra Type ◽  
Conditional Mean ◽  
Optimal Linear ◽  
Filtering Problem ◽  
Optimal Linear Filtering ◽  
Optimal Filtering Problem

The optimal filtering problem for multidimensional continuous possibly non-Markovian, Gaussian processes, observed through a linear channel driven by a Brownian motion, is revisited. Explicit Volterra type filtering equations involving the covariance function of the filtered process are derived both for the conditional mean and for the covariance of the filtering error. The solution of the filtering problem is applied to obtain a Cameron-Martin type formula for Laplace transforms of a quadratic functional of the process. Particular cases for which the results can be further elaborated are investigated.

Abstract Optimal Linear Filtering

2000 ◽  
Vol 38 (5) ◽  
pp. 1334-1352 ◽  
Author(s):  
Vladimir N. Fomin ◽  
Michael V. Ruzhansky
Keyword(s):  
Linear Filtering ◽  
Optimal Linear ◽  
Optimal Linear Filtering
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