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Bases in $ L\sb{2}$ spaces with applications to stochastic processes with orthogonal increments


Author: Stamatis Cambanis
Journal: Proc. Amer. Math. Soc. 29 (1971), 284-290
MSC: Primary 60.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0283862-2
MathSciNet review: 0283862
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Abstract: Orthonormal bases are explicitly given for $ {L_2}$ spaces on the real line. They are applied in obtaining orthogonal expansions for certain classes of stochastic processes and in constructing stochastic processes with orthogonal increments.


References [Enhancements On Off] (What's this?)

  • [1] N. I. Ahiezer and I. M. Glazman, Theory of linear operators in Hilbert space. Vol. 1, GITTL, Moscow, 1950; English transl., Ungar, New York, 1961. MR 13, 358. MR 0044034 (13:358b)
  • [2] J. Delporte, Functions aléatoires presque sûrement continues sur un intervalle fermé, Ann. Inst. H. Poincaré Sect. B 1 (1964/65), 111-215. MR 32 #493. MR 0183011 (32:493)
  • [3] I. I. Gihman and A. V. Skorohod, Introduction to the theory of random processes, ``Nauka", Moscow, 1965; English transl., Saunders, Philadelphia, Pa., 1969. MR 33 #6689; MR 40 #923. MR 0247660 (40:923)
  • [4] P. R. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1950. MR 11, 504. MR 0033869 (11:504d)
  • [5] T. Hida, Stationary stochastic processes, Princeton Univ. Press, Princeton, N. J., 1970. MR 0258106 (41:2753)
  • [6] P. Masani, Orthogonally scattered measures, Advances in Math. 2 (1968), 61-117. MR 37 #4231. MR 0228651 (37:4231)
  • [7] E. Masry, B. Liu and K. Steiglitz, Series expansion of wide-sense stationary random processes, IEEE Trans. Information Theory IT-14 (1968), 792-796. MR 38 #6660. MR 0238384 (38:6660)
  • [8] L. A. Shepp, Radon-Nikodým derivatives of Gaussian measures, Ann. Math. Statist. 37 (1966), 321-354. MR 32 #8408. MR 0190999 (32:8408)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0283862-2
Keywords: Bases in $ {L_2}$ spaces, orthogonal expansion of processes, processes with orthogonal increments
Article copyright: © Copyright 1971 American Mathematical Society

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