List of stochastic processes topics
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 . 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
- Queue
- 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
- v
- t
- e
- Additive process
- Bessel process
- Birth–death process
- Brownian motion
- Cauchy process
- Contact process
- Continuous-time random walk
- Cox process
- Diffusion process
- Dyson Brownian motion
- Empirical process
- Feller process
- Fleming–Viot process
- Gamma process
- Geometric process
- Hawkes 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
- Schramm–Loewner evolution
- Semimartingale
- Sigma-martingale
- Stable process
- Superprocess
- Telegraph process
- Variance gamma process
- Wiener process
- Wiener sausage
- Binomial options pricing model
- Black–Derman–Toy
- Black–Karasinski
- Black–Scholes
- Chan–Karolyi–Longstaff–Sanders (CKLS)
- Chen
- Constant elasticity of variance (CEV)
- Cox–Ingersoll–Ross (CIR)
- Garman–Kohlhagen
- Heath–Jarrow–Morton (HJM)
- Heston
- Ho–Lee
- Hull–White
- Korn-Kreer-Lenssen
- LIBOR market
- Rendleman–Bartter
- SABR volatility
- Vašíček
- Wilkie
- 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
- Zero–one laws (Blumenthal, Borel–Cantelli, Engelbert–Schmidt, Hewitt–Savage, Kolmogorov, Lévy)
- 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
- Stopping time
- Stratonovich integral
- Uniform integrability
- Usual hypotheses
- Wiener space
- Actuarial mathematics
- Control theory
- Econometrics
- Ergodic theory
- Extreme value theory (EVT)
- Large deviations theory
- Mathematical finance
- Mathematical statistics
- Probability theory
- Queueing theory
- Renewal theory
- Ruin theory
- Signal processing
- Statistics
- Stochastic analysis
- Time series analysis
- Machine learning
- List of topics
- Category