In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random...

In the mathematics of probability, a stochastic process is a random function. In practical applications, the domain over which the function is defined...

concept of a stochastic process is also referred to as a random process. Stochasticity is used in many different fields, including image processing, signal...

calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential...

In probability theory, a continuous stochastic process is a type of stochastic process that may be said to be "continuous" as a function of its "time"...

image processing, and telecommunications. The Poisson point process is often defined on the real number line, where it can be considered a stochastic process...

In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that...

Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals...

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...

statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for which the index variable takes...

manipulating statements according to certain rules. A key principle guiding this process is that whatever operation is applied to one side of an equation also needs...

statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking...

mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying certain regularity...

under a change in the sign of time. A stochastic process is reversible if the statistical properties of the process are the same as the statistical properties...

a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical...

Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or...

In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments:...

process (or Brownian motion, due to its historical connection with the physical process of the same name) is a real-valued continuous-time stochastic...

In mathematics, the Ornstein–Uhlenbeck process is a stochastic process with applications in financial mathematics and the physical sciences. Its original...

theory, a Cox process, also known as a doubly stochastic Poisson process is a point process which is a generalization of a Poisson process where the intensity...

Stochastic quantum mechanics is a framework for describing the dynamics of particles that are subjected to an intrinsic random processes as well as various...

probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability...

Predictable process, a stochastic process whose value is knowable Stochastic process, a random process, as opposed to a deterministic process Wiener process, a...

interchangeably. The definition of the autocorrelation coefficient of a stochastic process is: p.169  ρ X X ( t 1 , t 2 ) = K X X ⁡ ( t 1 , t 2 ) σ t 1 σ t 2...

Markov decision process (MDP), also called a stochastic dynamic program or stochastic control problem, is a model for sequential decision making when...

an Itō process that solves an associated stochastic differential equation. The link between semi-elliptic operators and stochastic processes, followed...

In stochastic analysis, a part of the mathematical theory of probability, a predictable process is a stochastic process whose value is knowable at a prior...

own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence...

Cauchy process is a type of stochastic process. There are symmetric and asymmetric forms of the Cauchy process. The unspecified term "Cauchy process" is...

In probability theory relating to stochastic processes, a Feller process is a particular kind of Markov process. Let X be a locally compact Hausdorff...