Second-Order Processes

  • Petar Todorovic
Part of the Springer Series in Statistics book series (SSS)


There exists a large class of engineering and physics problems whose solutions require only the knowledge of the first two moments and some very general properties of a second-order random process (see Definition 1.5.8). This chapter is concerned with some key properties of complex-valued second-order random processes.


Covariance Function Sample Function Ergodicity Property Stationary Stochastic Process Orthogonal Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cramér, H. (1940). On the theory of stationary random processes.Ann. Math. 41, 215–230.CrossRefGoogle Scholar
  2. Cramér, H. and Leadbetter, M.R. (1967). Stationary and Related Stochastic Processes. Wiley, New York.MATHGoogle Scholar
  3. Gihman, I.I. and Skorohod, A.V. (1974). The Theory of Stochastic Processes. Springer- Verlag, New York.MATHGoogle Scholar
  4. Grenander, U. and Rosenblatt, M. (1956). Statistical Analysis of Stationary Time Series. Wiley, New York.Google Scholar
  5. Karhunen, K. (1947). Über Lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann. Acad. Sci. Fenn. 37.Google Scholar
  6. Khinchin, A.Y. (1938). Correlation theory of stationary random processes. Usp. Math. Nauk. 5, 42–51.Google Scholar
  7. Loève, M. (1946). Fonctions aléatoires du second ordre. Rev. Sci. 84, 195–206.Google Scholar
  8. Lovitt, W.V. (1924). Linear Integral Equation. McGraw-Hill, New York.Google Scholar
  9. Mercer, J. (1909). Functions of positive and negative type and their connections with the theory of integral equations. Phil. Trans. Roy. Soc. London, Ser. A, 209, 415–446.CrossRefMATHGoogle Scholar
  10. Riesz, F., and Sz-Nagy, B. (1955). Functional Analysis. Frederic Unger Publishing, New York.Google Scholar
  11. Rozanov, A.Y. (1967). Stationary Random Processes. Holden-Day, San Francisco.MATHGoogle Scholar
  12. Tricomi, F.G. (1985). Integral Equation. Dover Publishing, New York.Google Scholar

Copyright information

© The Applied Probability Trust 1992

Authors and Affiliations

  • Petar Todorovic
    • 1
  1. 1.Department of Statistics and Applied ProbabilityUniversity of California—Santa BarbaraSanta BarbaraUSA

Personalised recommendations