WOLFRAM

Wolfram Language & System Documentation Center

Standard Deviation Function for Processes

The standard deviation function for a process is given by StandardDeviation[[t]].

A discrete-time and discrete-state random process:
Wolfram Language code: StandardDeviation[BinomialProcess[1 / 3][t]]
Wolfram Language code: DiscretePlot[%, {t, 0, 10}, ExtentSize -> 1 / 2, ColorFunction -> "Rainbow"]
A discrete-time and continuous-state random process:
Wolfram Language code: StandardDeviation[ARProcess[{2 / 3}, 1][t]]
Wolfram Language code: DiscretePlot[%, {t, 0, 10}, ExtentSize -> 1 / 2]
A continuous-time and discrete-state random process:
Wolfram Language code: StandardDeviation[PoissonProcess[2][t]]
Wolfram Language code: Plot[%, {t, 0, 10}, Filling -> Axis, ColorFunction -> "Rainbow"]
A continuous-time and continuous-state random process:
Wolfram Language code: StandardDeviation[WienerProcess[1, 1 / 2][t]]
Wolfram Language code: Plot[%, {t, 0, 10}, Filling -> Axis, ColorFunction -> "Rainbow"]