Itô calculusItô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations. The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes: where H is a locally square-integrable process adapted to the filtration generated by X , which is a Brownian motion or, more generally, a semimartingale.
SemimartingaleIn probability theory, a real valued stochastic process X is called a semimartingale if it can be decomposed as the sum of a local martingale and a càdlàg adapted finite-variation process. Semimartingales are "good integrators", forming the largest class of processes with respect to which the Itô integral and the Stratonovich integral can be defined. The class of semimartingales is quite large (including, for example, all continuously differentiable processes, Brownian motion and Poisson processes).
Arrow of timeThe arrow of time, also called time's arrow, is the concept positing the "one-way direction" or "asymmetry" of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This direction, according to Eddington, could be determined by studying the organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world ("a solid block of paper").
RadarRadar is a radiolocation system that uses radio waves to determine the distance (ranging), angle (azimuth), and radial velocity of objects relative to the site. It is used to detect and track aircraft, ships, spacecraft, guided missiles, and motor vehicles, and map weather formations, and terrain. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna (often the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the objects.
ValveA valve is a device or natural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways. Valves are technically fittings, but are usually discussed as a separate category. In an open valve, fluid flows in a direction from higher pressure to lower pressure. The word is derived from the Latin valva, the moving part of a door, in turn from volvere, to turn, roll.
Western paintingThe history of Western painting represents a continuous, though disrupted, tradition from antiquity until the present time. Until the mid-19th century it was primarily concerned with representational and Classical modes of production, after which time more modern, abstract and conceptual forms gained favor. Initially serving imperial, private, civic, and religious patronage, Western painting later found audiences in the aristocracy and the middle class. From the Middle Ages through the Renaissance painters worked for the church and a wealthy aristocracy.
Control valveA control valve is a valve used to control fluid flow by varying the size of the flow passage as directed by a signal from a controller. This enables the direct control of flow rate and the consequential control of process quantities such as pressure, temperature, and liquid level. In automatic control terminology, a control valve is termed a "final control element". The opening or closing of automatic control valves is usually done by electrical, hydraulic or pneumatic actuators.
