# 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*.