TransformedProcess

TransformedProcess[expr,xproc,t]

represents the transformed process of expr where the variable x follows the random process proc and t denotes the time.

TransformedProcess[expr,{x1proc1,x2proc2,},t]

represents a transformed process where x1, x2, are independent and follow the processes proc1, proc2, .

Details and Options

  • TransformedProcess is typically used to represent functional transformations of one or a finite number of time slices.
  • xproc can be entered as x dist proc or x[Distributed]proc.
  • The processes proci must all be discrete-time or continuous-time processes.
  • The expression expr must be a function of xi[fij[t]] for a finite number of different fij.
  • Assumptions on parameters can be specified using the option Assumptions->assum.
  • TransformedProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.

Examples

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Basic Examples  (1)

Define a transformed Wiener process:

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Simulate the process:

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Mean and variance functions:

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Covariance function:

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Scope  (8)

Options  (1)

Applications  (12)

Properties & Relations  (2)

Neat Examples  (2)

See Also

TransformedDistribution  Distributed  Probability  Expectation  RandomFunction

Introduced in 2014
(10.0)