Slice Distribution for Processes
Slice Distribution for Processes
A random process 
at time 
is a random variable 
given by its SliceDistribution. Below the slice distribution is plotted for a range of time values.
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, -3Sqrt[10] + 5, 3Sqrt[10] + 5}, AxesLabel -> Automatic, PlotRange -> All, MeshFunctions -> {#1&}, Mesh -> {Range[9]}, PlotPoints -> 50, ColorFunction -> "Rainbow", ImageSize -> Medium]