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Non-deterministic approaches in language studies are largely inspired by the work of Ferdinand de Saussure, for example, in functionalist linguistic theory, which argues that competence is based on performance. [37] [38] This distinction in functional theories of grammar should be carefully distinguished from the langue and parole distinction ...
A stochastic or random process can be defined as a collection of random variables that is indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the set. [4] [5] The set used to index the random variables is called the index set.
A stochastic program is an optimization problem in which some or all problem parameters are uncertain, but follow known probability distributions. [1] [2] This framework contrasts with deterministic optimization, in which all problem parameters are assumed to be known exactly. The goal of stochastic programming is to find a decision which both ...
Statistical models are often used even when the data-generating process being modeled is deterministic. For instance, coin tossing is, in principle, a deterministic process; yet it is commonly modeled as stochastic (via a Bernoulli process). Choosing an appropriate statistical model to represent a given data-generating process is sometimes ...
Stochastic computing is a collection of techniques that represent continuous values by streams of random bits. Complex computations can then be computed by simple bit-wise operations on the streams. Complex computations can then be computed by simple bit-wise operations on the streams.
Stochastic optimization also include methods with random iterates. Some hybrid methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. [ 1 ] Stochastic optimization methods generalize deterministic methods for deterministic problems.
In the former case of a unit root, stochastic shocks have permanent effects, and the process is not mean-reverting. In the latter case of a deterministic trend, the process is called a trend-stationary process, and stochastic shocks have only transitory effects after which the variable tends toward a deterministically evolving (non-constant) mean.
Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is ...