Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the relation between Green's functions and covariances of certain stochastic processes and its application to unbiased linear prediction


Authors: C. L. Dolph and M. A. Woodbury
Journal: Trans. Amer. Math. Soc. 72 (1952), 519-550
MSC: Primary 60.0X
MathSciNet review: 0050215
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] N. Wiener, The extrapolation, interpolation and smoothing of stationary time series, Wiley, 1946.
  • [2] A. Kolmogoroff, Interpolation und Extrapolation von stationären zufälligen Folgen, Bull. Acad. Sci. URSS Sér. Math. [Izvestia Akad. Nauk. SSSR] 5 (1941), 3–14 (Russian, with German summary). MR 0004416 (3,4e)
  • [3] R. S. Phillips and P. Weiss, Theoretical calculation on best smoothing of position data for gunnery prediction, NDRC Report 532, Massachusetts Institute of Technology Radiation Laboratory, 1944.
  • [4] L. B. C. Cunningham and W. R. B. Hynd, Random processes in problems of air warfare, Suppl. J. Roy. Statist. Soc. 8 (1946), 62–85. MR 0018378 (8,282a)
  • [5] J. L. Doob, The elementary Gaussian processes, Ann. Math. Statistics 15 (1944), 229–282. MR 0010931 (6,89a)
  • [6] E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757 (6,65f)
  • [7] P. Loève, Fonctions aléatoires du second ordre, A note in P. Lévy, Processus stochastiques et mouvement Brownien, Paris, Gauthier-Villars, 1948.
  • [8] G. E. Uhlenbeck and H. T. Wang, On the theory of Brownian motion, Review of Modern Physics vol. 17, nos. 22-23, pp. 323-342.
  • [9] R. Courant and D. Hilbert, Methoden der Mathematischen Physik. Vols. I, II, Interscience Publishers, Inc., N.Y., 1943. MR 0009069 (5,97b)
  • [10] Ralph Palmer Agnew, Differential equations, 2nd ed, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR 0114952 (22 #5761)
  • [11] H. W. Bode and C. E. Shannon, A simplified derivation of linear least square smoothing and prediction theory, Proc. I.R.E. 38 (1950), 417–425. MR 0034979 (11,672g)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60.0X

Retrieve articles in all journals with MSC: 60.0X


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1952-0050215-4
PII: S 0002-9947(1952)0050215-4
Article copyright: © Copyright 1952 American Mathematical Society