Causal Calculus in Terms of Brownian Motion

Part of the Applications of Mathematics book series (SMAP, volume 11)


In this chapter a new viewpoint of the analysis of non-linear functionals is presented, one which leads naturally to a generalisation of these functionals. Our approach is along the lines of the so-called causal analysis, where the passage of time is taken into account in the analysis of functionals of Brownian motion, and we begin the discussion by setting out our general point of view.


Brownian Motion Integral Representation Random Measure Reproduce Kernel Hilbert Space Functional Derivative 
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Copyright information

© Takeyuki Hida 1980

Authors and Affiliations

  • T. Hida
    • 1
  1. 1.Department of Mathematics Faculty of ScienceNagoya UniversityChikasu-Ku, Nagoya 464Japan

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