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keywords= process realization, RandomFunction, random path, random process, random process simulation, random realization, sample path, simulate random process, stochastic process;
description=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. ;

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mcp agent one api cag component apis core technologies of wolfram products wolfram language computable data wolfram notebooks linguistic understanding additional deployment options wolfram cloud wolfram web engine wolframscript wstpserver group organizational licensing all products consulting solutions we deliver solutions for the ai era combining symbolic computation data driven insights and deep technical expertise wolfram consulting data science finance business artificial intelligence data science healthcare real estate engineering civil engineering automotive engineering sustainable energy science technology agtech biosciences environmental science food science quantum computation social and behavioral sciences more wolfram solutions technology for education research universities colleges teaching universities high schools resources for students education initiatives next gen edtech computer based math more solutions for education contact us learning support get started wolfram language introduction fast intro for programmers fast intro for math students wolfram language documentation more learning highlighted core areas demonstrations youtube daily study groups wolfram schools and programs books grow your skills wolfram u courses in computing science life and more community learn solve problems and share ideas blog news views and insights from wolfram resources for software developers tech support contact us support faqs support faqs contact us company about wolfram career center all sites resources connect follow contact us work with us student ambassador initiative wolfram for startups student opportunities jobs using wolfram language educational programs for adults summer school winter school educational programs for youth middle school camp high school research program computational adventures read stephen wolfram s writings wolfram blog wolfram tech books wolfram media complex systems educational resources wolfram mathworld wolfram in stem wolfram challenges wolfram problem generator wolfram initiatives wolfram science wolfram foundation history of mathematics project events stephen wolfram livestreams online in person events contact us connect follow for ais wolfram cloud your account your account user portal wolfram cloud search close navigation menu products wolfram one mathematica system modeler compute services use with mathematica and wolfram one ai access use with mathematica and wolfram one finance platform wolfram alpha notebook edition application server enterprise private cloud wolfram engine wolfram player wolfram cloud app wolfram player app more mobile apps wolfram alpha wolfram alpha website wolfram alpha apis ai products wolfram ai ecosystem wolfram foundation tool wolfram cloud mcp wolfram local mcp agent one api cag component apis core technologies wolfram language computable data wolfram notebooks linguistic understanding additional deployment options wolfram cloud wolfram web engine wolframscript wstpserver group organizational licensing all products consulting solutions wolfram consulting data science finance business artificial intelligence data science healthcare real estate engineering civil engineering automotive engineering sustainable energy science technology agtech biosciences environmental science food science quantum computation social and behavioral sciences more wolfram solutions technology for education research universities colleges teaching universities high schools resources for students education initiatives next gen edtech computer based math more solutions for education contact us learning support get started wolfram language introduction fast intro for programmers fast intro for math students wolfram language documentation grow your skills wolfram u courses in computing science life and more community learn solve problems and share ideas blog news views and insights from wolfram resources for software developers tech support contact us support faqs more learning highlighted core areas demonstrations youtube daily study groups wolfram schools and programs books support faqs contact us company about wolfram career center all sites resources connect follow contact us work with us student ambassador initiative wolfram for startups student opportunities jobs using wolfram language educational programs for adults summer school winter school educational programs for youth middle school camp high school research program computational adventures read stephen wolfram s writings wolfram blog wolfram tech books wolfram media complex systems educational resources wolfram mathworld wolfram in stem wolfram challenges wolfram problem generator wolfram initiatives wolfram science wolfram foundation history of mathematics project events stephen wolfram livestreams online in person events contact us connect follow for ais wolfram cloud your account user portal enable javascript to interact with content and submit forms on wolfram websites learn how wolfram language system documentation center close randomfunction see also randomvariate slicedistribution stationarydistribution related guides random processes stochastic differential equation processes time series processes probability statistics queueing processes finite markov processes creating importing signals event series processing actuarial computation scientific models time event series data sources see also randomvariate slicedistribution stationarydistribution related guides random processes stochastic differential equation processes time series processes probability statistics queueing processes finite markov processes creating importing signals event series processing actuarial computation scientific models time event series data sources randomfunction proc t min t max generates a pseudorandom function from the process proc from t min to t max randomfunction proc t min t max dt generates a pseudorandom function from t min to t max in steps of dt randomfunction proc n generates an ensemble of n pseudorandom functions details and options examples basic examples scope basic uses parametric processes queueing processes finite markov processes time series processes stochastic differential equation processes transformations of random processes options workingprecision applications properties relations possible issues neat examples see also related guides history cite this page built in symbol see also randomvariate slicedistribution stationarydistribution related guides random processes stochastic differential equation processes time series processes probability statistics queueing processes finite markov processes creating importing signals event series processing actuarial computation scientific models time event series data sources see also randomvariate slicedistribution stationarydistribution related guides random processes stochastic differential equation processes time series processes probability statistics queueing processes finite markov processes creating importing signals event series processing actuarial computation scientific models time event series data sources randomfunction randomfunction proc t min t max generates a pseudorandom function from the process proc from t min to t max randomfunction proc t min t max dt generates a pseudorandom function from t min to t max 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 t 1 x t 1 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 all basic examples 5 simulate a discrete time and discrete state process wolfram language code randomfunction binomialprocess 1 3 0 50 wolfram language code listplot filling axis simulate a continuous time and discrete state process wolfram language code randomfunction poissonprocess 1 0 10 wolfram language code liststepplot filling axis simulate a discrete time and continuous state process wolfram language code randomfunction arprocess 0 7 1 0 50 wolfram language code listplot filling axis axesorigin 0 0 simulate a continuous time and continuous state process wolfram language code randomfunction wienerprocess 0 10 0 1 wolfram language code listlineplot filling axis axesorigin 0 0 simulate an ensemble of 10 paths wolfram language code randomfunction wienerprocess 0 10 0 1 10 wolfram language code listlineplot scope 21 basic uses 6 randomfunction returns a temporaldata object wolfram language code sample randomfunction poissonprocess 3 4 0 7 obtain the random path wolfram language code sample path simulate a vector valued process wolfram language code proc arprocess 1 2 3 2 1 3 3 0 0 2 path randomfunction proc 40 path up to time 10 wolfram language code normal path 1 10 visualize the path on the plane wolfram language code parametricplot timeseries path t t 0 40 axesorigin 0 0 colorfunction function x y t colordata avocadocolors t estimate the parameters for a random process using a sample path wolfram language code data randomfunction randomwalkprocess 3 0 10 3 wolfram language code findprocessparameters data randomwalkprocess p use a simulation to find the expected path wolfram language code data randomfunction ornsteinuhlenbeckprocess 0 3 3 2 0 10 5 10 2 wolfram language code sim listlineplot data joined true calculate the mean for each time stamp wolfram language code mean timeseriesthread mean data wolfram language code show sim listlineplot mean joined true plotstyle directive thick yellow use a simulation to find confidence bands for a random path wolfram language code data randomfunction renewalprocess gammadistribution 2 3 0 50 10 2 wolfram language code sim listlineplot data joined true calculate the standard error bands for each time stamp wolfram language code sd1 timeseriesthread mean standarddeviation data sd2 timeseriesthread mean standarddeviation data wolfram language code show sim listlineplot sd1 sd2 joined true plotstyle directive dashed yellow simulate an ensemble of 1000 paths wolfram language code data randomfunction wienerprocess 1 1 2 0 10 0 1 10 3 compute data slices from paths and plot their distribution shapes wolfram language code distributionchart table data slicedata t t 1 10 compute slice distributions at the same time stamps and plot their distribution shapes wolfram language code distributionchart table randomvariate wienerprocess 1 1 2 t 10 3 t 1 10 parametric processes 3 simulate a bernoulli process wolfram language code data randomfunction bernoulliprocess 3 4 0 30 wolfram language code listplot data filling axis simulate a wiener process wolfram language code data randomfunction wienerprocess 2 7 0 1 0 01 wolfram language code listlineplot filling axis simulate a compound poisson process with an exponential jump size distribution wolfram language code 𝒫 compoundpoissonprocess 7 exponentialdistribution 2 1 wolfram language code data randomfunction 𝒫 0 20 wolfram language code liststepplot data filling axis queueing processes 2 simulate an m m 1 queue with different arrival and service rates wolfram language code randomfunction queueingprocess 3 5 0 15 wolfram language code liststepplot filling axis simulate a closed queueing network wolfram language code 𝒬 queueingnetworkprocess 0 0 0 0 0 3 0 7 1 0 0 1 0 0 1 0 5 1 25 1 1 1 10 wolfram language code randomfunction 𝒬 0 50 wolfram language code liststepplot filling axis finite markov processes 1 simulate a discrete time finite markov process wolfram language code 𝒫 discretemarkovprocess 1 0 0 0 1 2 1 2 1 2 0 1 2 1 2 1 2 0 wolfram language code data randomfunction 𝒫 0 30 wolfram language code listplot data filling axis ticks automatic 1 2 3 simulate a discrete time hidden markov process wolfram language code proc hiddenmarkovprocess 0 3 0 7 0 95 0 05 0 1 0 9 normaldistribution 1 1 0 3 normaldistribution 2 4 0 5 wolfram language code data randomfunction proc 0 100 100 wolfram language code histogram data automatic pdf time series processes 5 simulate a moving average process wolfram language code randomfunction maprocess 3 1 1 10 path simulate an autoregressive process wolfram language code sample randomfunction arprocess 2 3 1 1 100 wolfram language code listplot sample filling axis simulate an autoregressive moving average process with given precision wolfram language code randomfunction armaprocess 1 10 3 10 2 10 1 6 workingprecision 9 path simulate a few integrated autoregressive moving average processes wolfram language code sample randomfunction arimaprocess 2 3 1 2 1 1 1 100 3 wolfram language code listplot sample filling axis simulate a vector valued sarima time series wolfram language code a 4 3 3 4 b 2 5 2 3 σ 1 0 0 3 seedrandom 4 sample randomfunction sarimaprocess 1 b 12 a 1 σ 1 10 2 data timeseries sample resamplingmethod automatic create a 3d sample path function with time wolfram language code f data pathfunction g t_ numericq join t f t the color function depends on time wolfram language code parametricplot3d g t t 1 100 colorfunction function t x y colordata bluegreenyellow t plotstyle thick boxratios 1 aspectratio 1 2 stochastic differential equation processes 2 simulate an ito process wolfram language code 𝒫 itoprocess ⅆx t x t ⅆt ⅆw t x t x 0 t 0 w wienerprocess wolfram language code randomfunction 𝒫 0 5 0 01 wolfram language code listlineplot filling axis simulate a stratonovich process wolfram language code 𝒫 stratonovichprocess ⅆx t x t ⅆt sqrt 1 x t 2 ⅆw t x t x 1 t w wienerprocess wolfram language code randomfunction 𝒫 0 5 0 01 wolfram language code listlineplot filling axis transformations of random processes 2 square of a poisson process wolfram language code 𝒫 transformedprocess p t 2 p poissonprocess 1 t simulate the process wolfram language code data randomfunction 𝒫 0 30 0 1 3 wolfram language code liststepplot data sum of a wiener process and a geometric brownian motion process wolfram language code 𝒫 transformedprocess w t g t w wienerprocess g geometricbrownianmotionprocess 0 1 2 t simulate the process wolfram language code data randomfunction 𝒫 0 10 0 1 3 wolfram language code listlineplot data plotrange all options 1 workingprecision 1 generate a sample path w...