Why do we fix $\omega$ in the definition of a sample path of a stochastic process? If $f:T \to \Omega$ is an arbitrary function, can't we define sample path to be equal to $\{X(t, f(t)): t \in T\}$?
2026-04-01 12:49:54.1775047794
definition of a sample path of a stochastic process
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