May 2015
Intermediate to advanced
384 pages
9h 20m
English
book
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
by Tailen Hsing, Randall Eubank
Content preview from Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
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Chapter 1Introduction
Briefly stated, a stochastic process is an indexed collection of random variables all of which are defined on a common probability space 
. If we denote the index set by 
, then this can be described mathematically as
where 
is a 
-measurable function on the sample space 
. The 
argument will generally be suppressed and 
will typically be shortened to just 
.
Once the 
have been observed for every , the process has been realized and the resulting collection of real numbers is ...
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