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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