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Stochastic Variable Theory

  • John R. Klauder
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Let X(t) be a random function of time t, where t Є [a,b], − ∞ < a < b < ∞ or t Є [a; [),or t Є (−∞, ∞), as the specific case dictates. One way to describe the observable properties of the set of random functions, a.k.a. (also known as) a stochastic variable, is by means of a collection of correlation functions
$${C}_{l}({t}_{1}, {t}_{2}, \ldots , {t}_{l})\equiv \langle X ({t}_{1}) X ({t}_{2}) \ldots X ({t}_{l}) \rangle, $$
for all \(l \geq 1\) If the functions in the set {C l } are pointwise defined, then X(l) is called a stochastic process. On the other hand, if the functions in the set are distributional in nature, then X(l is called a generalized stochastic process. We will have occasion to discuss both types.

Keywords

Correlation Function Brownian Motion Gaussian Process Erential Equation Wiener Process 
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.

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Copyright information

© Birkhäuser Boston 2011

Authors and Affiliations

  1. 1.Department of Physics and Department of MathematicsUniversity of FloridaGainesvilleUSA

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