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# Analytic Properties of Random Processes

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Properties  ::  Continuity  ::  Differentiation  ::  Integration

## Integration

For a function , we define a Riemann integral as

where and .

Let us define a similar sort of limit for a random process. We will define the limits in the mean-square sense. Then

is the mean-square integral of .

Properties of M.S. integrals :

1. The integral exists if and only if

2. Assume that exists. Then .
3. .
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 07). Analytic Properties of Random Processes. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lecture7_4.htm. This work is licensed under a Creative Commons License