RandomFunction[BinomialProcess[1/3],{0,50}]

ListPlot[%,Filling->Axis]

RandomFunction[ARProcess[{0.7},1],{0,50}]

ListPlot[RandomFunction[ARProcess[{0.7},1],{0,50}],Filling->Axis,AxesOrigin->{0,0}]

RandomFunction[PoissonProcess[1],{0,10}]

ListLinePlot[%,Filling->Axis,InterpolationOrder->0]

RandomFunction[WienerProcess[],{0,10,0.1}]

ListLinePlot[RandomFunction[WienerProcess[],{0,10,0.1}],Filling->Axis,AxesOrigin->{0,0}]