It is natural to see the simulation as a deterministic function that maps these " inputs " into a collection of " outputs ".
2.
Where a and b are deterministic functions, t is a differential in time, and ? is a random draw from a standard normal distribution at each instant.
3.
With a search algorithm, subrandom numbers can be used to find the cumulative distribution of a statistical distribution, and all local minima and all solutions of deterministic functions.
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It is therefore sometimes said that the expansion is " bi-orthogonal " since the random coefficients are orthogonal in the probability space while the deterministic functions are orthogonal in the time domain.
5.
The Poisson process model for jumps is that the probability of one jump in the interval is plus higher order terms . could be a constant, a deterministic function of time, or a stochastic process.
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Applications that don't involve sorting would be in finding the mean, standard deviation, skewness and kurtosis of a statistical distribution, and in finding the integral and global maxima and minima of difficult deterministic functions.
7.
Most database management systems restrict check constraints to a single row, with access to constants and deterministic functions, but not to data in other tables, or to data invisible to the current transaction because of transaction isolation.
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Since in local volatility models the volatility is a deterministic function of the random stock price, local volatility models are not very well used to price cliquet options or forward start options, whose values depend specifically on the random nature of volatility itself.
9.
Broadly, utility theory assumes that ( 1 ) users and suppliers have perfect information about the market; ( 2 ) they have deterministic functions ( faced with the same options, they will always make the same choices ); and ( 3 ) switching between alternatives is costless.
10.
Note that the assumption of a joint probability distribution allows us to model uncertainty in predictions ( e . g . from noise in data ) because y is not a deterministic function of x, but rather a random variable with conditional distribution P ( y | x ) for a fixed x.
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