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.

Stochastic processes topics

This list is currently incomplete. See also Stochastic_processes

• Bernoulli process 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 Birth-death process
• Branching process Branching process
• Brownian bridge Brownian bridge
• Brownian motion Brownian motion
• Chinese restaurant process Chinese restaurant process
• CIR process CIR process
• Continuous stochastic process Continuous stochastic process
• Cox process Cox process
• Dirichlet processes
• Finite-dimensional distribution Finite-dimensional distribution
• Galton–Watson process Galton–Watson process
• Gamma process Gamma process
• Gaussian process Gaussian process - processes where all linear combinations of coordinates are normally distributed random variables.
• Gauss-Markov process Gauss-Markov process (cf. below)
• Girsanov's theorem 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 Lévy process
• Local time (mathematics) Local time
• Loop-erased random walk 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
• Continuous-time Markov process Continuous-time Markov process
• Markov process Markov process
• Semi-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 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, $f(A)\; le\; f(B)$ with probability 1.
• Poisson process Poisson process
• Compound Poisson process Compound Poisson process
• Population process Population process
• Queueing theory Queueing theory
• Queue Queue
• Random field Random field
• Gaussian random field Gaussian random field
• Markov random field Markov random field
• Sample continuous process Sample continuous process
• Stationary process Stationary process
• Stochastic calculus Stochastic calculus
• Itō calculus Itō calculus
• Malliavin calculus Malliavin calculus
• Semimartingale Semimartingale
• Stratonovich integral Stratonovich integral
• Stochastic differential equation Stochastic differential equation
• Stochastic process Stochastic process
• Telegraph process Telegraph process
• Time series Time series
• Wiener process Wiener process