BUILT-IN MATHEMATICA SYMBOL

# RandomFunction

RandomFunction[proc, {tmin, tmax}]
generates a pseudorandom function from the process proc from to .

RandomFunction[proc, {tmin, tmax, dt}]
generates a pseudorandom function from to in steps of dt.

RandomFunction[proc, ..., n]
generates an ensemble of n pseudorandom functions.

## Details and OptionsDetails and Options

• RandomFunction returns a TemporalData object that can be used to extract several properties including the paths consisting of time-value pairs .
• For discrete-time processes such as BinomialProcess or ARMAProcess, the step dt is taken to be .
• 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 Mathematica. You can start with a particular seed, using SeedRandom.
• The following options can be given:
•  Method Automatic what method to use WorkingPrecision Automatic precision used in internal computations
• With the setting , random numbers of precision p will be generated.
• Special settings for Method are documented under the individual random process reference pages.

## ExamplesExamplesopen allclose all

### Basic Examples (5)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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