mathematical space वाक्य
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- Often this space is " d "-dimensional Euclidean space denoted here by \ textstyle \ textbf { R } ^ { d }, although point processes can be defined on more mathematical spaces.
- But the Poisson point process can be defined on the n-dimensional Euclidean space or other mathematical spaces, where it is often interpreted as a random set or a random counting measure, instead of a stochastic process.
- In statistics and probability theory, a "'point process "'is a collection of mathematical points randomly located on some underlying mathematical space such as the real line, the Cartesian plane, or more abstract spaces.
- A Poisson point process is defined on some underlying mathematical space, called a "'carrier space "', or "'state space "', though the latter term has a different meaning in the context of stochastic processes.
- Since these processes are often used to represent collections of points randomly scattered in space, time or both, the underlying space is usually " d "-dimensional Euclidean space denoted here by "'R "'d, but they can be defined on more abstract mathematical spaces.
- Since these processes are often used to represent collections of points randomly scattered in space, time or both, the underlying space is usually " d "-dimensional Euclidean space denoted here by \ textstyle \ textbf { R } ^ { d }, but they can be defined on more abstract mathematical spaces.
- Since these processes are often used to represent collections of points randomly scattered in physical space, time or both, the underlying space is usually " d "-dimensional Euclidean space denoted here by \ textstyle \ textbf { R } ^ { d }, but they can be defined on more abstract mathematical spaces.
- The Poisson point process can be defined, studied and used in one dimension, for example, on the real line, where it can be interpreted as a counting process or part of a queueing model; in higher dimensions such as the plane where it plays a role in stochastic geometry or on more general mathematical spaces.
- In other words, for each point of the original Poisson process, there is an independent and identically distributed non-negative random variable, and then the compound Poisson process is then formed from the sum of all the random variables corresponding to points of the Poisson process located in a some region of the underlying mathematical space.
- In physics and mathematics, the "'dimension "'of a mathematical space ( or object ) is informally defined as the minimum number of coordinates needed to specify any dimension of two because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere.
- The phrase " "'H " " control "'comes from the name of the mathematical space over which the optimization takes place : " H " " is the space of SISO systems, this is effectively the maximum magnitude of the frequency response . ) " H " " techniques can be used to minimize the closed loop impact of a perturbation : depending on the problem formulation, the impact will either be measured in terms of stabilization or performance.
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