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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Randall Eubank, Tailen Hsing

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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 c01-math-0001. If we denote the index set by c01-math-0002, then this can be described mathematically as

equation

where c01-math-0004 is a c01-math-0005-measurable function on the sample space c01-math-0006. The c01-math-0007 argument will generally be suppressed and c01-math-0008 will typically be shortened to just c01-math-0009.

Once the c01-math-0010 have been observed for every , the process has been realized and the resulting collection of real numbers is ...

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