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, the Wolfram Language 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.

Simulation & Estimation

(RefLink[RandomFunction, paclet:ref/RandomFunction]) — simulate a random process

(RefLink[TemporalData, paclet:ref/TemporalData]) — represent one or several time-series data

(RefLink[EstimatedProcess, paclet:ref/EstimatedProcess]), (RefLink[FindProcessParameters, paclet:ref/FindProcessParameters]) — estimate process parameters from data

Process Distributions

(RefLink[Probability, paclet:ref/Probability]) — compute probabilities of predicates of process state at different times

(RefLink[SliceDistribution, paclet:ref/SliceDistribution]) — process state distribution at time t

(RefLink[StationaryDistribution, paclet:ref/StationaryDistribution]) — process state distribution at time ∞

Process Moments

(RefLink[Mean, paclet:ref/Mean]) — mean function for a process

(RefLink[CovarianceFunction, paclet:ref/CovarianceFunction]) — covariance function for a process

(RefLink[WeakStationarity, paclet:ref/WeakStationarity]) — conditions for a process to be weakly stationary

(OrangeLink[Parametric Processes », paclet:guide/ParametricRandomProcesses])

(OrangeLink[Derived Processes », paclet:guide/DerivedRandomProcesses])

(OrangeLink[Markov Processes », paclet:guide/MarkovProcesses])

(OrangeLink[Queueing Processes », paclet:guide/QueueingProcesses])

(OrangeLink[Time-Series Processes », paclet:guide/TimeSeriesProcesses])

(OrangeLink[Stochastic Differential Equation Processes », paclet:guide/StochasticDifferentialEquationProcesses])