Stochastic processes

In probability theory, a martingale is a model of a fair game where knowledge of past events never helps predict the mean of the future winnings.

In probability theory and statistics, a Gaussian process is a statistical model where observations occur in a continuous domain, e.

Brownian motion or pedesis (from Ancient Greek: πήδησις /pέːdεːsis/ "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving atoms or molecules in the gas or liquid.

Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone, by using Bayesian inference and estimating a joint probability distribution over the variables for each timeframe.

In mathematics, a filtration is an indexed set Si of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that if i ≤ j in I, then Si ⊆ Sj.

The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments.

A random walk is a mathematical object which describes a path that consists of a succession of random steps.

In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random and independent, and statistically identical over different time intervals of the same length.

A stochastic event or system is one that is unpredictable because of a random variable.

In mathematics, a Feller-continuous process is a continuous-time stochastic process for which the expected value of suitable statistics of the process at a given time in the future depend continuously on the initial condition of the process.

In probability theory relating to stochastic processes, a Feller process is a particular kind of Markov process.

In probability theory, a balance equation is an equation that describes the probability flux associated with a Markov chain in and out of states or set of states.

In mathematics, the Ornstein–Uhlenbeck process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction.

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" or index parameter.