stochastic motion

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• Stochastic cooling — is a form of particle beam cooling. It is used in some particle accelerators and storage rings to control the emittance of the particle beams in the machine. This process uses the electrical signals that the individual charged particles generate… …   Wikipedia

• Stochastic volatility — models are used in the field of quantitative finance to evaluate derivative securities, such as options. The name derives from the models treatment of the underlying security s volatility as a random process, governed by state variables such as… …   Wikipedia

• Stochastic — (from the Greek Στόχος for aim or guess ) means random.A stochastic process is one whose behavior is non deterministic in that a state s next state is determined both by the process s predictable actions and by a random element. Stochastic crafts …   Wikipedia

• Stochastic calculus — is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave… …   Wikipedia

• Stochastic differential equation — A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process. SDE are used to model diverse phenomena such as… …   Wikipedia

• Stochastic process — A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or deterministic system) in probability theory. Instead of dealing with only one possible reality of how the process might evolve under time (as is… …   Wikipedia

• Stochastic processes and boundary value problems — In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani s 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion.… …   Wikipedia

• Brownian motion — This article is about the physical phenomenon; for the stochastic process, see Wiener process. For the sports team, see Brownian Motion (Ultimate). For the mobility model, see Random walk. Brownian motion (named after the botanist Robert Brown)… …   Wikipedia

• Infinitesimal generator (stochastic processes) — In mathematics mdash; specifically, in stochastic analysis mdash; the infinitesimal generator of a stochastic process is a partial differential operator that encodes a great deal of information about the process. The generator is used in… …   Wikipedia

• Fractional Brownian motion — A normalized fractional Brownian motion (denoted fBm) B^H(t) on [0,T] , Tin mathbb{R} is a continuous time Gaussian process starting at zero, with mean zero, and having the following correlation function::E [B^H(t) B^H(s)] =frac{1}{2}… …   Wikipedia

• List of stochastic processes topics — In the mathematics of probability, a stochastic process can be thought of as 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… …   Wikipedia