List of stochastic processes topics

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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 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, ƒ(A) ≤ ƒ(B) with probability 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

* v
* t
* e

Stochastic processes

Discrete time|

* Bernoulli process
* Branching process
* Chinese restaurant process
* Galton–Watson process
* Independent and identically distributed random variables
* Markov chain
* Moran process
* Random walk
* Loop-erased
* Self-avoiding
* Biased
* Maximal entropy

Continuous time|

* Bessel process
* Birth–death process
* Brownian motion
* Bridge
* Excursion
* Fractional
* Geometric
* Meander
* Cauchy process
* Contact process
* Continuous-time random walk
* Cox process
* Diffusion process
* Empirical process
* Feller process
* Fleming–Viot process
* Gamma process
* Geometric process
* Hunt process
* Interacting particle systems
* Itô diffusion
* Itô process
* Jump diffusion
* Jump process
* Lévy process
* Local time
* Markov additive process
* McKean–Vlasov process
* Ornstein–Uhlenbeck process
* Poisson process
* Compound
* Non-homogeneous
* Point process
* Schramm–Loewner evolution
* Semimartingale
* Sigma-martingale
* Stable process
* Superprocess
* Telegraph process
* Variance gamma process
* Wiener process
* Wiener sausage

Both|

* Branching process
* Galves–Löcherbach model
* Gaussian process
* Hidden Markov model (HMM)
* Markov process
* Martingale
* Differences
* Local
* Sub-
* Super-
* Random dynamical system
* Regenerative process
* Renewal process
* Stochastic chains with memory of variable length
* White noise

Fields and other|

* Dirichlet process
* Gaussian random field
* Gibbs measure
* Hopfield model
* Ising model
* Potts model
* Boolean network
* Markov random field
* Percolation
* Pitman–Yor process
* Point process
* Cox
* Poisson
* Random field
* Random graph

Time series models|

* Autoregressive conditional heteroskedasticity (ARCH) model
* Autoregressive integrated moving average (ARIMA) model
* Autoregressive (AR) model
* Autoregressive–moving-average (ARMA) model
* Generalized autoregressive conditional heteroskedasticity (GARCH) model
* Moving-average (MA) model

Financial models|

* Black–Derman–Toy
* Black–Karasinski
* Black–Scholes
* Chen
* Constant elasticity of variance (CEV)
* Cox–Ingersoll–Ross (CIR)
* Garman–Kohlhagen
* Heath–Jarrow–Morton (HJM)
* Heston
* Ho–Lee
* Hull–White
* LIBOR market
* Rendleman–Bartter
* SABR volatility
* Vašíček
* Wilkie

Actuarial models|

* Bühlmann
* Cramér–Lundberg
* Risk process
* Sparre–Anderson

Queueing models|

* Bulk
* Fluid
* Generalized queueing network
* M/G/1
* M/M/1
* M/M/c

Properties|

* Càdlàg paths
* Continuous
* Continuous paths
* Ergodic
* Exchangeable
* Feller-continuous
* Gauss–Markov
* Markov
* Mixing
* Piecewise deterministic
* Predictable
* Progressively measurable
* Self-similar
* Stationary
* Time-reversible

Limit theorems|

* Central limit theorem
* Donsker's theorem
* Doob's martingale convergence theorems
* Ergodic theorem
* Fisher–Tippett–Gnedenko theorem
* Large deviation principle
* Law of large numbers (weak/strong)
* Law of the iterated logarithm
* Maximal ergodic theorem
* Sanov's theorem

Inequalities|

* Burkholder–Davis–Gundy
* Doob's martingale
* Kunita–Watanabe

Tools|

* Cameron–Martin formula
* Convergence of random variables
* Doléans-Dade exponential
* Doob decomposition theorem
* Doob–Meyer decomposition theorem
* Doob's optional stopping theorem
* Dynkin's formula
* Feynman–Kac formula
* Filtration
* Girsanov theorem
* Infinitesimal generator
* Itô integral
* Itô's lemma
* Karhunen–Loève_theorem
* Kolmogorov continuity theorem
* Kolmogorov extension theorem
* Lévy–Prokhorov metric
* Malliavin calculus
* Martingale representation theorem
* Optional stopping theorem
* Prokhorov's theorem
* Quadratic variation
* Reflection principle
* Skorokhod integral
* Skorokhod's representation theorem
* Skorokhod space
* Snell envelope
* Stochastic differential equation
* Tanaka
* Stopping time
* Stratonovich integral
* Uniform integrability
* Usual hypotheses
* Wiener space
* Classical
* Abstract

Disciplines|

* Actuarial mathematics
* Econometrics
* Ergodic theory
* Extreme value theory (EVT)
* Large deviations theory
* Mathematical finance
* Mathematical statistics
* Probability theory
* Queueing theory
* Renewal theory
* Ruin theory
* Statistics
* System on Chip design
* Stochastic analysis
* Time series analysis
* Machine learning

* List of topics
* Category

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