Continuous-Time and Continuous-State Processes
Continuous-Time and Continuous-State Processes
procs1 = {WienerProcess[1, .5], GeometricBrownianMotionProcess[0, .1, 2], BrownianBridgeProcess[0.1, {0, 0}, {10, 2}], OrnsteinUhlenbeckProcess[0, .1, .3], CoxIngersollRossProcess[.3, .5, 1, 2], FractionalBrownianMotionProcess[.3], ItoProcess[ⅆx[t] == -x[t]ⅆt + 0.5Sqrt[1 + x[t] ^ 2]ⅆw[t], x[t], {x, 1}, t, wWienerProcess[]], StratonovichProcess[ⅆx[t] == -x[t]ⅆt + 0.5Sqrt[1 + x[t] ^ 2]ⅆw[t], x[t], {x, 1}, t, wWienerProcess[]]};
procs2 = {CompoundPoissonProcess[.8, NormalDistribution[]], CompoundRenewalProcess[GammaDistribution[2, 1.7], NormalDistribution[]]};data1 = RandomFunction[#, {0, 10, 0.1}]& /@ procs1;
data2 = RandomFunction[#, {0, 10}]& /@ procs2;plots1 = Table[ListLinePlot[data1[[i]], PlotLabel -> Head[procs1[[i]]], Filling -> Axis, PlotRange -> All, Ticks -> None, FillingStyle -> Directive[Opacity[0.5], RandomChoice[ColorData[45, "ColorList"]]]], {i, Length[procs1]}];
plots2 = Table[ListLinePlot[data2[[i]], PlotLabel -> Head[procs2[[i]]], Filling -> Axis, PlotRange -> All, InterpolationOrder -> 0, Ticks -> None, FillingStyle -> Directive[Opacity[0.5], RandomChoice[ColorData[45, "ColorList"]]]], {i, Length[procs2]}];
plots = Join[plots1, plots2]