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Random process (Rev #8, changes)

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Contents

Idea

This The page theory is of about stochastic or random processes is the application of probability theory to situations where the random objects are functions. If one focuses on quantities that can be observed about a funcion, such as its pointwise values, its integrals against given test functions, its extreme values, and so on, a means stochastic process is just an uncountable collection of modelling random in variables engineering satisfying applications consistency and conditions sciences, coming especially from the fact that the random variables are all observations of a function rather than a disparate collection of variables.climate models.

Random processes are a broad topic in both pure mathematical research and applications, applications. which This we page cannot is even about touch random here, processes but as we’ll a mention means some of references modelling to in the engineering general applications theory. and sciences, especiallyclimate models. As such, most often the random function is a function of continuous time, time ordering and continuity play an important role, and one considers dynamical equations with random coefficients and/or driven by noise. These stochastic differential equations are the primary “consistency conditions” linking all the random variables associated with a stochastic process. One may also consider random fields which are a function of spatial coordinates, not time, or evolving random fields where the random function is a function of both time and space coordinates.

Implementation Issues

A computer model of a random process needs a random number generator. Certain random processes are solutions of stochastic differential equations and can therefore be simulated by numerical solvers of these equations.

References

General

Terence Tao? has written about measure theory on abstract spaces and random processes, they are part of these online lecture notes:

Probability Theory