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

probability theory, the formal concept of a stochastic process is also referred to as a random process. Stochasticity is used in many different fields, including...

manipulate statements are used to achieve this. A key principle guiding this process is that whatever operation is applied to one side of an equation also needs...

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

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

statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional...

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...

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"...

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

science. The Poisson point process is often defined on the real number line, where it can be considered a stochastic process. It is used, for example,...

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

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

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 Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on...

In mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his...

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

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

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...

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

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...

interchangeably. The definition of the auto-correlation 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...

In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the...

diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature...

between point processes and stochastic processes is not clear. Others consider a point process as a stochastic process, where the process is indexed by...

Galton–Watson process is a branching stochastic process arising from Francis Galton's statistical investigation of the extinction of family names. The process models...

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

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which...

In physics, statistics, econometrics and signal processing, a stochastic process is said to be in an ergodic regime if an observable's ensemble average...

theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time...

jointly wide sense stationary stochastic processes can be estimated by averaging the product of samples measured from one process and samples measured from...