Simulate Any Random Process 

RandomFunction can be used to simulate any random process.

A discrete-time and discrete-state random process.

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

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X RandomFunction[BinomialProcess[1/3], {0, 50}]; ListPlot[%, Filling -> Axis]

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A discrete-time and continuous-state random process.

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

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

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A continuous-time and discrete-state random process.

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

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X RandomFunction[PoissonProcess[1], {0, 10}]; ListLinePlot[%, Filling -> Axis, InterpolationOrder -> 0]

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A continuous-time and continuous-state random process.

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

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

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