# List of stochastic processes topics

List of stochastic processes topics

In the mathematics of probability, a stochastic process can be thought of as 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.

tochastic processes topics

* 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.
* Birth-death process
* Branching process
* Brownian bridge
* Brownian motion
* Chinese restaurant process
* CIR process
* Continuous stochastic process
* Cox process
*Dirichlet processes
* Finite-dimensional distribution
* Galton&ndash;Watson process
* Gamma process
* Gaussian process - processes 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
* Ornstein-Uhlenbeck process
*Point processes: random arrangements of points in a space $S$. 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, $f\left(A\right) le f\left(B\right)$ with probability 1.
* Poisson process
** Compound Poisson process
* Population process
* Queueing theory
** Queue
* Random field
** Gaussian random field
** Markov random field
* Sample continuous process
* Stationary process
* Stochastic calculus
** Itō calculus
** Malliavin calculus
** Semimartingale
** Stratonovich integral
* Stochastic differential equation
* Stochastic process
* Telegraph process
* Time series
* Wiener process

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