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:
-
Method Automatic what method to use WorkingPrecision Automatic precision 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
open all close allBasic Examples (5)
Scope (21)
Basic Uses (6)
RandomFunction returns a TemporalData object:
Simulate a vector-valued process:
Visualize the path on the plane:
Estimate the parameters for a random process using a sample path:
Use a simulation to find the expected path:
Calculate the mean for each time stamp:
Use a simulation to find confidence bands for a random path:
Calculate the standard error bands for each time stamp:
Simulate an ensemble of 1000 paths:
Compute data slices from paths and plot their distribution shapes:
Compute slice distributions at the same time stamps and plot their distribution shapes:
Parametric Processes (3)
Queueing Processes (2)
Finite Markov Processes (1)
Time Series Processes (5)
Stochastic Differential Equation Processes (2)
Options (1)
WorkingPrecision (1)
Generate a sample path with default machine precision:
Use WorkingPrecision to generate a sample path with higher precision:
Applications (4)
Visualize a transformed process:
Simulate solutions of the stochastic differential equation 
:
Define the values of the parameters:
Simulate the Wiener process paths:
The solution as function of a path:
Estimate unknown slice distribution of a random process:
Probability density function of slice distribution is not known in closed form:
Generate a random sample of paths:
Extract values from all paths at time 
:
Visualize its probability density function:
Test if it fits a standard normal distribution:
Approximate an ARIMAProcess with fixed initial conditions by an ARMAProcess:
Properties & Relations (1)
RandomFunction generates a path for a random process:
Use RandomVariate to generate a sample for a time slice of the process:
Use Histogram to estimate probability density:
Possible Issues (3)
Neat Examples (3)
Simulate a WienerProcess in two dimensions:
Simulate a symmetric random walk in 2D:
Simulate a weakly stationary three-dimensional ARMAProcess:
Text
Wolfram Research (2012), RandomFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomFunction.html.
CMS
Wolfram Language. 2012. "RandomFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomFunction.html.
APA
Wolfram Language. (2012). RandomFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomFunction.html