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The index set of this stochastic process is the non-negative numbers, while its state space is three-dimensional Euclidean space. ... The theory of stochastic ...
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 ...
Among the list of new applications in mathematics there are new approaches to probability, [11] hydrodynamics, [21] measure theory, [22] nonsmooth and harmonic analysis, [23] etc. There are also applications of nonstandard analysis to the theory of stochastic processes, particularly constructions of Brownian motion as random walks.
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 ...
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
What distinguishes a statistical model from other mathematical models is that a statistical model is non-deterministic. Thus, in a statistical model specified via mathematical equations, some of the variables do not have specific values, but instead have probability distributions; i.e. some of the variables are stochastic. In the above example ...
According to whether all the model variables are deterministic, economic models can be classified as stochastic or non-stochastic models; according to whether all the variables are quantitative, economic models are classified as discrete or continuous choice model; according to the model's intended purpose/function, it can be classified as quantitative or qualitative; according to the model's ...
The linear no-threshold model (LNT) is a dose-response model used in radiation protection to estimate stochastic health effects such as radiation-induced cancer, genetic mutations and teratogenic effects on the human body due to exposure to ionizing radiation. The model assumes a linear relationship between dose and health effects, even for ...