In this definition, it has been assumed that the stochastic variables are scalar-valued.
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In such system we find certain stochastic variable x which assume values that depend on time.
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While the mean values are taken as predictable variables determined by dynamics laws, the turbulent fluctuations are regarded as stochastic variables.
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Conversely, in an "'indirect dilution assay "'the dose levels are administered at fixed dose levels, so that the response is a stochastic variable.
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Where " W " is a stochastic variable ( Wiener process : Basic properties ); a good discrete analogue for " W " is a simple random walk.
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Simon's result that decision makers only focus on " expected values " of stochastic variables was very sensitive to the assumed structure of the problem, hence indirectly on the formulation of expectations.
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It concerns the statistics of a system of N particles, such that the number of possible states for the systems grow as 2 ^ N, while the energy of such states is a Gaussian stochastic variable.
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In a "'direct dilution assay "'the amount of dose needed to produce a specific ( fixed ) response is measured, so that the dose is a stochastic variable defining the "'tolerance distribution " '.
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To compute the long-term average or expected value of a stochastic variable Y, for each state S j and time t k there is a contribution of Y j, k �P ( S = S j, t = t k ).
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A useful spin-off of the method is the combined use of time-dependent coupled cluster method and boson-mapping of stochastic variables to provide a rigorous and systematic cluster expansion method for monitoring quantum dynamics of systems strongly perturbed by colored noise.
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