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Stochastic effect, or "chance effect" is one classification of radiation effects that refers to the random, statistical nature of the damage. In contrast to the deterministic effect, severity is independent of dose. Only the probability of an effect increases with dose.
For example, if {():} is a stochastic process with state space and index set = [,), then for any two non-negative numbers [,) and [,) such that , the difference is a -valued random variable known as an increment.
Stochastic health effects are those that occur by chance, and whose probability is proportional to the dose, but whose severity is independent of the dose. [3] The LNT model assumes there is no lower threshold at which stochastic effects start, and assumes a linear relationship between dose and the stochastic health risk.
A non-stochastic or deterministic health effect has a severity that is dependent on dose and is believed to have a threshold level for which no effect is seen. Stochastic health effects occur by chance, generally occurring without a threshold level of dose, whose probability is proportional to the dose and whose severity is independent of the ...
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.
Stochastic mechanics is the framework concerned with the construction of such stochastic processes that generate a probability measure for quantum mechanics. For a Brownian motion, it is known that the statistical fluctuations of a Brownian particle are often induced by the interaction of the particle with a large number of microscopic particles.
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, [1] resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices , [ 2 ] random ...
Deterministic vs. probabilistic (stochastic). A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions.