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.

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ReferenceReference

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 ▪ ...

Stochastic Differential Equation Processes »

ItoProcess ▪ StratonovichProcess ▪ ...

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