This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. L. Campbell, A series expansion for random processes, I.E.E.E. Trans. Information Theory, vol. IT-12 (1966), p. 271.
E. Masry, K. Steiglitz, and B. Liu, Bases in Hilbert space related to the representation of stationary operators, SIAM J. Appl. Math., vol. 16(1968), pp. 552–562.
E. Masry, B. Liu, and K. Steiglitz, Series expansion of wide-sense stationary random processes, to appear in I.E.E.E. Trans. Information Theory.
E. Parzen, An approach to time series analysis, Ann. Math. Statist., vol. 32 (1961), pp. 951–989.
E. Parzen, Extraction and detection problems and reproducing kernel Hilbert spaces, SIAM J. Control vol. 1 (1962), pp. 35–62.
E. Parzen, Probability density functionals and reproducing kernel Hilbert spaces, in Time Series Analysis, M. Rosenblatt, editor, 1963, John Wiley and Sons, New York, pp. 155–169.
J. Capon, Radon Nikodym derivatives of stationary gaussian measures, Ann. Math. Statist., vol. 35 (1964), pp. 517–531.
T. Kailath, Some results on singular detection, Information and Control, vol. 9 (1966), pp. 130–152.
T. Kailath, A projection method for signal detection in colored Gaussian noise, I.E.E.E. Trans. Information Theory, vol. IT-13 (1967), pp 441–447.
N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., vol. 68 (1950), pp. 337–404.
J. L. Doob, Stochastic Processes, John Wiley and Sons, New York, 1953.
I. Selin, Detection Theory, Princeton University Press, Princeton, N. J., 1965.
E. C. Titchmarsh, Theory of Functions, 2nd ed., Oxford University Press, London 1939.
K. Yao, Applications of reproducing kernel Hilbert spaces—bandlimited signal models, Information and Control, vol. 11 (1967), pp. 429–444.
W. Magnus and F. Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, 2nd ed., Springer-Verlag, Berlin, 1948.
D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty—I, Bell System Tech, J. vol. 40 (1961), pp. 43–63.
E. J. Kelly, I. S. Reed, and W. L. Root, The detection of radar echoes in noise I, J. Soc. Indust. Appl. Math., vol. 8 (1960), pp. 309–341.
W. L. Root, Asymptotic forms of detectors of signals in noise, Mathematics Research Center, University of Wisconsin, Technical Summary Report no. 456, 1964.
U. Grenander and G. Szegö, Toeplitz forms and their Applications, University of California Press, Los Angeles, 1958.
S. Kullback, Information Theory and Statistics, John Wiley and Sons, New York, 1959.
A. Rényi, Wahrscheinlichkeitsrechnung, mit einem Anhang über Informationstheorie, Deutscher Verlag der Wissenschaften, Berlin, 1962.
E. A. Robinson, Random Wavelets and Cybernetic Systems, Charles Griffin and Co., London, 1962.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1969 Springer-Verlag
About this paper
Cite this paper
Campbell, L.L. (1969). Series expansions for random processes. In: Behara, M., Krickeberg, K., Wolfowitz, J. (eds) Probability and Information Theory. Lecture Notes in Mathematics, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079118
Download citation
DOI: https://doi.org/10.1007/BFb0079118
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-04608-0
Online ISBN: 978-3-540-36098-8
eBook Packages: Springer Book Archive