sample function

Let {X(t)tT} be a stochastic processMathworldPlanetmath, where X(t) is a random variableMathworldPlanetmath on the probability spaceMathworldPlanetmath (Ω,,𝐏). Writing X(t) as X(t,ω), where tT and ωΩ, we see that if we fix the sample point ω, we have a function in t: Xω(t):tX(t). This function Xω(t) of t is called a sample function, or sample path of the stochastic process.

Title sample function
Canonical name SampleFunction
Date of creation 2013-03-22 15:21:15
Last modified on 2013-03-22 15:21:15
Owner gel (22282)
Last modified by gel (22282)
Numerical id 5
Author gel (22282)
Entry type Definition
Classification msc 60G17
Classification msc 60G05
Defines sample path