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Random Processes
A random process models the progression of a system over time, where the evolution is random rather than deterministic. The key point is that observations that are close in time are dependent, and this can be used to model, simulate, and predict the behavior of the process. Random processes are used in a variety of fields including economics, finance, engineering, physics, and biology.
Building on its strong capabilities for distributions, Mathematica provides cohesive and comprehensive random process support. Using a symbolic representation of a process makes it easy to simulate its behavior, estimate parameters from data, and compute state probabilities at different times. There is additional functionality for special classes of random processes such as Markov chains, queues, time series, and stochastic differential equations.
Featured Examples |
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Accuracy of Approximation Schemes
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Analyze a Tennis Game
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Analyze Time Series Model Residuals
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Brownian Motion
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Coin Flip Sequences
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Compute Correlation and Partial Correlation Functions
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Compute Moments Symbolically
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Continuous-Time and Continuous-State Processes
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Continuous-Time and Discrete-State Processes
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Covariance Function for Processes
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Discrete-Time and Continuous-State Processes
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Discrete-Time and Discrete-State Processes
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Email Arrivals
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Estimate Process Parameters from Data
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Expected Profit from an Option
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Find Conditions for Stationarity and Invertibility of Time Series Processes
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Fit Time Series Processes to Data
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Forecast Exchange Rates
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Generate an Ensemble of Paths
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Global Warming
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Heston Model
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Hubble Gyroscope Maintenance
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Ito and Stratonovich Solutions of the Linear Growth Model
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Machine Repair Problem
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Mean, Median, and Variance Functions from Data
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Model Seasonal Data
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Particle Moving between Two Barriers
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Perform Autoregressive Filtering
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Perform Spectral Analysis of a Time Series
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Radioactive Emission
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RLC Circuit Driven by Periodic Signal and White Noise
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Simulate Any Random Process
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Simulate Time Series Data
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Simulate Zero Coupon Bond Using Chen's Model
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Simulation of Processes Driven by Vector Noise Process
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Slice Distribution for Processes
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Slice Distributions from Data
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Stationary Distribution for Finite Markov Processes
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Stochastic Differential Equation for Exponential Decay
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Stochastic Logistic Growth Model
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Structural Properties of Finite Markov Processes
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Test for Integrated Time Series
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Visualize a Sample Path for a Finite Markov Process
Reference
Simulation & Estimation
RandomFunction — simulate a random process
TemporalData — represent one or several time-series data
EstimatedProcess, FindProcessParameters — estimate process parameters from data
Process Distributions
Probability — compute probabilities of predicates of process state at different times
SliceDistribution — process state distribution at time 
StationaryDistribution — process state distribution at time 
ProcessParameterAssumptions ▪ ProcessParameterQ
Process Moments
Mean — mean function for a process
CovarianceFunction — covariance function for a process
WeakStationarity — conditions for a process to be weakly stationary
CorrelationFunction ▪ AbsoluteCorrelationFunction
Parametric Processes »
RandomWalkProcess ▪ PoissonProcess ▪ WienerProcess ▪ ...
Markov Processes »
DiscreteMarkovProcess ▪ ContinuousMarkovProcess ▪ ...
Queueing Processes »
QueueingProcess ▪ QueueingNetworkProcess ▪ ...
Time-Series Processes »
ARMAProcess ▪ SARIMAProcess ▪ ...
