In the mathematics of probability, a stochastic process is a random function. In practical applications, the domain over which the function is defined is a time interval (time series) or a region of space (random field).

Familiar examples of time series include stock market and exchange rate fluctuations, signals such as speech, audio and video; medical data such as a patient's EKG, EEG, blood pressure or temperature; and random movement such as Brownian motion or random walks.

Examples of random fields include static images, random topographies (landscapes), or composition variations of an inhomogeneous material.

Stochastic processes topics

:This list is currently incomplete. See also :Category:Stochastic processes

  • Basic affine jump diffusion
  • Bernoulli process: discrete-time processes with two possible states.
  • Bernoulli schemes: discrete-time processes with N possible states; every stationary process in N outcomes is a Bernoulli scheme, and vice versa.
  • Bessel process
  • Birth–death process
  • Branching process
  • Branching random walk
  • Brownian bridge
  • Brownian motion
  • Chinese restaurant process
  • CIR process
  • Continuous stochastic process
  • Cox process
  • Dirichlet processes
  • Finite-dimensional distribution
  • First passage time
  • Galton–Watson process
  • Gamma process
  • Gaussian process – a process where all linear combinations of coordinates are normally distributed random variables.
  • Gauss–Markov process (cf. below)
  • GenI process
  • Girsanov's theorem
  • Hawkes process
  • Homogeneous processes: processes where the domain has some symmetry and the finite-dimensional probability distributions also have that symmetry. Special cases include stationary processes, also called time-homogeneous.
  • Karhunen–Loève theorem
  • Lévy process
  • Local time (mathematics)
  • Loop-erased random walk
  • Markov processes are those in which the future is conditionally independent of the past given the present.
  • Markov chain
  • Markov chain central limit theorem
  • Continuous-time Markov process
  • Markov process
  • Semi-Markov process
  • Gauss–Markov processes: processes that are both Gaussian and Markov
  • Martingales – processes with constraints on the expectation
  • Onsager–Machlup function
  • Ornstein–Uhlenbeck process
  • Percolation theory
  • Point processes: random arrangements of points in a space <math>S</math>. They can be modelled as stochastic processes where the domain is a sufficiently large family of subsets of S, ordered by inclusion; the range is the set of natural numbers; and, if A is a subset of B, &fnof;(A)&nbsp;≤&nbsp;&fnof;(B) with probability&nbsp;1.
  • Poisson process
  • Compound Poisson process
  • Population process
  • Probabilistic cellular automaton
  • Queueing theory
  • Queue
  • Random field
  • Gaussian random field
  • Markov random field
  • Sample-continuous process
  • Stationary process
  • Stochastic calculus
  • Itô calculus
  • Malliavin calculus
  • Semimartingale
  • Stratonovich integral
  • Stochastic control
  • Stochastic differential equation
  • Stochastic process
  • Telegraph process
  • Time series
  • Wald's martingale
  • Wiener process