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.
RandomFunction — simulate a random process
TemporalData — represent one or several time-series data
Probability — compute probabilities of predicates of process state at different times
SliceDistribution — process state distribution at time
StationaryDistribution — process state distribution at time
Mean — mean function for a process
CovarianceFunction — covariance function for a process
WeakStationarity — conditions for a process to be weakly stationary