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
edit- 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 . 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, ƒ(A) ≤ ƒ(B) with probability 1.
- Poisson process
- Population process
- Probabilistic cellular automaton
- Queueing theory
- Random field
- Sample-continuous process
- Stationary process
- Stochastic calculus
- Stochastic control
- Stochastic differential equation
- Stochastic process
- Telegraph process
- Time series
- Wald's martingale
- Wiener process
