# List of stochastic processes topics

From Infogalactic: the planetary knowledge core

In the mathematics of probability, a **stochastic process** is a random function. In practical applications, the domain over which the function is defined as 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.

- Bernoulli schemes: discrete-time processes with
- 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)

- Girsanov's theorem
- 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
- 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