SliceDistribution[BinomialProcess[2/3],t]

DiscretePlot3D[PDF[%,x],{t,0,10},{x,0,10},ExtentSize->1/2,PlotStyle->EdgeForm[Opacity[0.3]],FillingStyle->Opacity[0.4],AxesLabel->Automatic,ColorFunction->"Rainbow",ImageSize->Medium]

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

Plot3D[Evaluate[PDF[%,x]Sum[UnitBox[2(t-i)],{i,0,10}]],{t,-0.5,10.5},{x,-5,5},MeshFunctions->{#1&},Mesh->{Sort[Join[Range[0,10]-0.25,Range[0,10]+0.25]]},MeshShading->{None,Automatic},Exclusions->{Sin[π (t-0.25)],Sin[π (t+0.25)]},AxesLabel->Automatic,BoundaryStyle->None,ColorFunction->"Rainbow",ImageSize->Medium]

SliceDistribution[PoissonProcess[1],t]

Plot3D[Evaluate[PDF[%,Floor[x-0.25]]Sum[UnitBox[2(x-i)],{i,0,10}]],{t,1,10},{x,-0.5,10.5},MeshFunctions->{#2&},Mesh->{Sort[Join[Range[0,10]-0.25,Range[0,10]+0.25]]},MeshShading->{None,Automatic},Exclusions->{Sin[π (x-0.25)],Sin[π (x+0.25)]},AxesLabel->Automatic,PlotRange->All,PlotPoints->75,BoundaryStyle->None,Ticks->{Automatic,Range[0,10,5],Automatic},ColorFunction->"Rainbow",ImageSize->Medium]

SliceDistribution[WienerProcess[1,1],t]

Plot3D[PDF[%,x],{t,1,10},{x,-3(Sqrt[10])+5,3(Sqrt[10])+5},AxesLabel->Automatic,PlotRange->All,MeshFunctions->{#1&},Mesh->{Range[9]},PlotPoints->50,ColorFunction->"Rainbow",ImageSize->Medium]