StandardDeviation[BinomialProcess[1/3][t]]

DiscretePlot[%,{t,0,10},ExtentSize->1/2,ColorFunction->"Rainbow"]

StandardDeviation[ARProcess[{2/3},1][t]]

DiscretePlot[%,{t,0,10},ExtentSize->1/2]

StandardDeviation[PoissonProcess[2][t]]

Plot[%,{t,0,10},Filling->Axis,ColorFunction->"Rainbow"]

StandardDeviation[WienerProcess[1,1/2][t]]

Plot[%,{t,0,10},Filling->Axis,ColorFunction->"Rainbow"]