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)
• 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 ${\displaystyle S}$. 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