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.
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:
-
- 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)
Simulate a discrete-time and discrete-state process:
Simulate a continuous-time and discrete-state process:
Simulate a discrete-time and continuous-state process:
Simulate a continuous-time and continuous-state process:
Simulate an ensemble of 10 paths:
Scope (21)
Basic Uses (6)
RandomFunction returns a TemporalData object:
Obtain the random path:
Simulate a vector-valued process:
Path up to time 10:
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)
Simulate a Bernoulli process:
Simulate a Wiener process:
Simulate a compound Poisson process with an exponential jump size distribution:
Queueing Processes (2)
Simulate an M/M/1 queue with different arrival and service rates:
Simulate a closed queueing network:
Finite Markov Processes (1)
Simulate a discrete-time finite Markov process:
Simulate a discrete-time hidden Markov process:
Time Series Processes (5)
Simulate a moving-average process:
Simulate an autoregressive process:
Simulate an autoregressive moving-average process with given precision:
Simulate a few integrated autoregressive moving-average processes:
Simulate a vector-valued SARIMA time series:
Create a 3D sample path function with time:
The color function depends on time:
Stochastic Differential Equation Processes (2)
Simulate an Ito process:
Simulate a Stratonovich process:
Transformations of Random Processes (2)
Square of a Poisson process:
Simulate the process:
Sum of a Wiener process and a geometric Brownian motion process:
Simulate the process:
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 the 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 :
Use sample paths to assess the approximation:
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)
The length of a step must be smaller than the domain length:
Use a step length less than 1 to get a sample path:
Continuous-time processes require a step to be specified:
Specify a step:
Discrete-time processes do not accept a step specification:
Step is 1 by default:
Neat Examples (3)
Simulate a WienerProcess in two dimensions:
Simulate a symmetric random walk in 2D:
In 3D:
Simulate a weakly stationary three-dimensional ARMAProcess :
Non-weakly stationary process, starting at the origin:
History
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
BibTeX
@misc{reference.wolfram_2025_randomfunction, author="Wolfram Research", title="{RandomFunction}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/RandomFunction.html}", note=[Accessed: 06-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_randomfunction, organization={Wolfram Research}, title={RandomFunction}, year={2012}, url={https://reference.wolfram.com/language/ref/RandomFunction.html}, note=[Accessed: 06-December-2025]}