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Volumn 18, Issue 4, 1972, Pages 473-481

Orthogonal Functionals of the Poisson Process

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EID: 84918385534     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1972.1054856     Document Type: Article
Times cited : (125)

References (21)
  • 1
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • N. Wiener, “The homogeneous chaos,” Amer. J. Math., vol. 60, pp. 897-936, 1938.
    • (1938) Amer. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 2
    • 84941501572 scopus 로고
    • Cambridge, Mass.: M.I.T. Press, and New York: Wiley
    • Nonlinear Problems in Random Theory. Cambridge, Mass.: M.I.T. Press, and New York: Wiley, 1958.
    • (1958) Nonlinear Problems in Random Theory
  • 3
    • 84972503912 scopus 로고
    • Multiple Wiener integral
    • also “Spectral type of shift transformations of differential process with stationary increments, ”Trans. Amer. Math. Soc., vol. 81, pp. 253-263, 1956.
    • K. Itô, “Multiple Wiener integral,” J. Math. Soc. Japan, vol. 13, no. 1, pp. 157–169, 1951; also “Spectral type of shift transformations of differential process with stationary increments,” Trans. Amer. Math. Soc., vol. 81, pp. 253-263,1956.
    • (1951) J. Math. Soc. Japan , vol.13 , Issue.1 , pp. 157-169
    • Itô, K.1
  • 4
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Apr.
    • R. H. Cameron and W. T. Martin, “The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals,” Ann. Math., vol. 48, pp. 385–392, Apr. 1947.
    • (1947) Ann. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 5
    • 0346618319 scopus 로고
    • Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral
    • pt. I. Berkeley and Los Angeles, Calif.: Univ. California Press
    • T. Hida and N. Ikeda, “Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral,” in Proc. 5th Berkeley Symp. Mathematical Statistics and Probability, vol. 2, pt. I. Berkeley and Los Angeles, Calif.: Univ. California Press, 1965, pp. 117–143.
    • (1965) Proc. 5th Berkeley Symp. Mathematical Statistics and Probability , vol.2 , pp. 117-143
    • Hida, T.1    Ikeda, N.2
  • 6
    • 25644451590 scopus 로고
    • Special functions connected with representations of the infinite dimensional motion group
    • N. Kôno “Special functions connected with representations of the infinite dimensional motion group,” J. Math. Kyoto Univ., vol. 6, no. 1, pp, 61–83, 1966.
    • (1966) J. Math. Kyoto Univ. , vol.6 , Issue.1 , pp. 61-83
    • Kôno, N.1
  • 7
    • 84941512727 scopus 로고
    • On Hermite polynomials
    • (mimeo circular in Japanese)
    • “On Hermite polynomials,” in Seminar on Probabilitys vol. 27, (mimeo circular in Japanese), 1967.
    • (1967) Seminar on Probabilitys , vol.27
  • 8
    • 0004911282 scopus 로고
    • Symbolic calculu. of the Wiener process and Wiener-Hermite functionals
    • T. Imamura, W. C. Meecham, and A. Siegel, “Symbolic calculu. of the Wiener process and Wiener-Hermite functionals,” J, Math. Phys., vol. 6, no. 5, pp. 695–706, 1965.
    • (1965) J. Math. Phys. , vol.6 , Issue.5 , pp. 695-706
    • Imamura, T.1    Meecham, W.C.2    Siegel, A.3
  • 9
    • 0013201447 scopus 로고
    • Wiener-Hermite expansion in model turbulence in the late decay stage
    • A Siegel, T. Imamura, and W. C. Meecham, “Wiener-Hermite expansion in model turbulence in the late decay stage,” J. Math. Phys., vol. 6, no. 5, pp, 707-721, 1965.
    • (1965) J. Math. Phys. , vol.6 , Issue.5 , pp. 707-721
    • Siegel, A.1    Imamura, T.2    Meecham, W.C.3
  • 13
    • 0004073954 scopus 로고
    • New York: Amer. Math. Soc., Coll. Publ
    • G. Szegö Orthogonal Polynomials. New York: Amer. Math. Soc., Coll. Publ., 1939.
    • (1939) Orthogonal Polynomials
    • Szegö, G.1
  • 14
    • 84980073665 scopus 로고
    • Note on N-dimensional Hermite polynomials
    • Dec
    • H. Grad, “Note on N-dimensional Hermite polynomials,” Commun. Pure Appl. Math., vol. 2, pp. 325-330, Dec, 1949.
    • (1949) Commun. Pure Appl. Math. , vol.2 , pp. 325-330
    • Grad, H.1
  • 19
    • 84914974921 scopus 로고
    • Optimal nonlinear filtering for independent increment processes-Part I
    • Oct. îº, “Optimal nonlinear filtering for independent increment processes-Part II,” ibid., vol. IT-13, pp. 568-578, Oct. 1967.
    • J. R. Fisher and E. B. Stear, “Optimal nonlinear filtering for independent increment processes-Part I,” IEEE Trans. Inform. Theory, vol. IT-I3, pp. 558–568, Oct. 1967; îº, “Optimal nonlinear filtering for independent increment processes-Part II,” ibid., vol. IT-13, pp. 568-578, Oct. 1967.
    • (1967) IEEE Trans. Inform. Theory , vol.IT-I3 , pp. 558-568
    • Fisher, J.R.1    Stear, E.B.2
  • 20
    • 84954868205 scopus 로고
    • Hermite functional expansions and the calculation of output autocorrelation and spectrum for any time-invariant nonlinear system with noise input
    • J. F. Barrett, “Hermite functional expansions and the calculation of output autocorrelation and spectrum for any time-invariant nonlinear system with noise input,” J. Electron. Contr., vol. 16 no. 1, pp. 107–113, 1964.
    • (1964) J. Electron. Contr. , vol.16 , Issue.1 , pp. 107-113
    • Barrett, J.F.1
  • 21
    • 0000661335 scopus 로고
    • The use of functionals in the analysis of non-linear physical systems
    • J. F. Barrett, “The use of functionals in the analysis of non-linear physical systems,” J. Electron. Contr., vol. 15, no. 6, pp. 567–615, 1963.
    • (1963) J. Electron. Contr. , vol.15 , Issue.6 , pp. 567-615
    • Barrett, J.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.