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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.
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.
Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, [a] used by Louis Bachelier to study price changes on the Paris Bourse, [21] and the Poisson process, used by A. K. Erlang to study the number of ...
A simple example may help to explain how the Gillespie algorithm works. Consider a system of molecules of two types, A and B . In this system, A and B reversibly bind together to form AB dimers such that two reactions are possible: either A and B react reversibly to form an AB dimer, or an AB dimer dissociates into A and B .
An animated example of a Brownian motion-like random walk on a torus. In the scaling limit, random walk approaches the Wiener process according to Donsker's theorem. In mathematics, Brownian motion is described by the Wiener process, a continuous-time stochastic process named in honor of Norbert Wiener.
A stochastic pump is a classical stochastic system that responds with nonzero, on average, currents to periodic changes of parameters. The stochastic pump effect can be interpreted in terms of a geometric phase in evolution of the moment generating function of stochastic currents.
In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing how a system evolves when subjected to a combination of deterministic and fluctuating ("random") forces. The dependent variables in a Langevin equation typically are collective (macroscopic) variables changing only slowly in comparison ...
Stochastic thermodynamics can be applied to driven (i.e. open) quantum systems whenever the effects of quantum coherence can be ignored. The dynamics of an open quantum system is then equivalent to a classical stochastic one. However, this is sometimes at the cost of requiring unrealistic measurements at the beginning and end of a process. [c] [13]