RandomFunction

RandomFunction[proc,{tmin,tmax}]

generates a pseudorandom function from the process proc from tmin to tmax.

RandomFunction[proc,{tmin,tmax,dt}]

generates a pseudorandom function from tmin to tmax in steps of dt.

RandomFunction[proc,, n]

generates an ensemble of n pseudorandom functions.

Details and Options

  • RandomFunction returns a TemporalData object that can be used to extract several properties including the paths consisting of time-value pairs {{t1,x[t1]},}.
  • For discrete-time processes such as BinomialProcess or ARMAProcess, the step dt is taken to be 1.
  • For continuous-time processes with jumps, such as PoissonProcess and QueueingProcess, the step dt is random and given by the process itself.
  • For continuous-time processes without jumps, such as WienerProcess and ItoProcess, an explicit dt needs to be given.
  • RandomFunction gives a different random function whenever you run the Wolfram Language. You can start with a particular seed, using SeedRandom.
  • The following options can be given:
  • MethodAutomaticwhat method to use
    WorkingPrecisionAutomaticprecision used in internal computations
  • With the setting WorkingPrecision->p, random numbers of precision p will be generated.
  • Special settings for Method are documented under the individual random process reference pages.

Examples

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Basic Examples  (5)

Simulate a discrete-time and discrete-state process:

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Simulate a continuous-time and discrete-state process:

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Simulate a discrete-time and continuous-state process:

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Simulate a continuous-time and continuous-state process:

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Simulate an ensemble of 10 paths:

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Scope  (21)

Options  (1)

Applications  (4)

Properties & Relations  (1)

Possible Issues  (3)

Neat Examples  (3)

See Also

RandomVariate  SliceDistribution  StationaryDistribution

Introduced in 2012
(9.0)