Wiener-Hopf method
Righteous hack for certain integral equations
May 5, 2021 — May 5, 2021
dynamical systems
linear algebra
probability
signal processing
state space models
statistics
stochastic processes
time series
Placeholder.
- Wiener-Hopf Method – from Wolfram MathWorld
- Wiener-Hopf method
- Integral equation of convolution type
1 References
Bacry, and Muzy. 2016. “First- and Second-Order Statistics Characterization of Hawkes Processes and Non-Parametric Estimation.” IEEE Transactions on Information Theory.
Crighton, Dowling, Williams, et al. 1992. “Wiener-Hopf Technique.” In Modern Methods in Analytical Acoustics: Lecture Notes.
Doney. 2007. Fluctuation Theory for Lévy Processes: Ecole d’eté de Probabilités de Saint-Flour XXXV, 2005. Lecture Notes in Mathematics 1897.
Gohberg, and Kaashoek. 1991. “The State Space Method for Solving Singular Integral Equations.” In Mathematical System Theory: The Influence of R. E. Kalman.
Green, and Anderson. 1986. “On the Continuity of the Wiener-Hopf Factorization Operation.”
Hawkes. 1971. “Point Spectra of Some Mutually Exciting Point Processes.” Journal of the Royal Statistical Society. Series B (Methodological).
Kailath, T., Geesey, and Weinert. 1972. “Some Relations Among RKHS Norms, Fredholm Equations, and Innovations Representations.” IEEE Transactions on Information Theory.
Kailath, Thomas, Sayed, and Hassibi. 2000. Linear Estimation. Prentice Hall Information and System Sciences Series.
Kyprianou. 2014. Fluctuations of Lévy Processes with Applications: Introductory Lectures. Universitext.
Lawrie, and Abrahams. 2007. “A Brief Historical Perspective of the Wiener–Hopf Technique.” Journal of Engineering Mathematics.
Najafabadi, and Kucerovsky. 2015. “A Weak Approximation for the Wiener–Hopf Factorization.” Edited by Kok Lay Teo. Cogent Mathematics.
Noble. 1958. Methods based on the Wiener-Hopf technique for the solution of partial differential equations.
Parzen. 1962. “Extraction and Detection Problems and Reproducing Kernel Hilbert Spaces.” Journal of the Society for Industrial and Applied Mathematics Series A Control.
Polyanin, and Manzhirov. 1998. Handbook of Integral Equations.
Sayed, and Kailath. 2001. “A Survey of Spectral Factorization Methods.” Numerical Linear Algebra with Applications.
Youla, Bongiorno, and Jabr. 1976. “Modern Wiener–Hopf Design of Optimal Controllers Part I: The Single-Input-Output Case.” IEEE Transactions on Automatic Control.