procs={BernoulliProcess[1/3],BinomialProcess[1/3],RandomWalkProcess[1/3],DiscreteMarkovProcess[{1,0,0},{{0,(1/2),(1/2)},{(1/2),0,(1/2)},{(1/2),(1/2),0}}],RenewalProcess[PascalDistribution[1,1/3]],CompoundRenewalProcess[PascalDistribution[1,1/3],BinomialDistribution[5,1/2]]};

data=RandomFunction[#,{0,25}]&/@procs;

Table[ListPlot[data[[i]],PlotLabel->Head[procs[[i]]],Filling->Axis,FillingStyle->RandomChoice[ColorData[45,"ColorList"]]],{i,Length[procs]}]