Calculus in Mean Square

  • Peter A. Ruymgaart
  • Tsu T. Soong
Part of the Springer Series in Information Sciences book series (SSINF, volume 14)


Having introduced the concept of a stochastic process in Sect. 1.4, some elements of calculus in mean square, or m.s. calculus, are discussed in this chapter to the extent required for Chap. 3. Since the class of stochastic processes to be considered contains real functions as a special case, some of this development is also applicable to ordinary real functions.


Strong Sense Cauchy Sequence Weak Sense Convergent Sequence Intermediate Point 
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  1. 2.1
    M. Loéve: Probability Theory (Van Nostrand, New York 1963)MATHGoogle Scholar
  2. 2.2
    T. T. Soong: Random Differential Equations in Science and Engineering (Academic, New York 1973)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Peter A. Ruymgaart
    • 1
  • Tsu T. Soong
    • 2
  1. 1.Department of MathematicsUniversity of Technology, DelftDelftThe Netherlands
  2. 2.Faculty of Engineering and Applied SciencesState University of New York at BuffaloBuffaloUSA

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