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  2. Stochastic differential equation - Wikipedia

    en.wikipedia.org/wiki/Stochastic_differential...

    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 ...

  3. Stochastic quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Stochastic_quantum_mechanics

    Stochastic mechanics is a framework for describing the dynamics of particles that are subjected to an intrinsic random processes as well as various external forces. The framework provides a derivation of the diffusion equations associated to these stochastic particles.

  4. Stochastic process - Wikipedia

    en.wikipedia.org/wiki/Stochastic_process

    The definition of a stochastic process varies, [67] but a stochastic process is traditionally defined as a collection of random variables indexed by some set. [ 68 ] [ 69 ] The terms random process and stochastic process are considered synonyms and are used interchangeably, without the index set being precisely specified.

  5. Stochastic - Wikipedia

    en.wikipedia.org/wiki/Stochastic

    The term stochastic process first appeared in English in a 1934 paper by Joseph L. Doob. [1] For the term and a specific mathematical definition, Doob cited another 1934 paper, where the term stochastischer Prozeß was used in German by Aleksandr Khinchin, [22] [23] though the German term had been used earlier in 1931 by Andrey Kolmogorov. [24]

  6. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    A stochastic differential equation (SDE) is an equation in which the unknown quantity is a stochastic process and the equation involves some known stochastic processes, for example, the Wiener process in the case of diffusion equations. A stochastic partial differential equation (SPDE) is an equation that generalizes SDEs to include space-time ...

  7. Langevin equation - Wikipedia

    en.wikipedia.org/wiki/Langevin_equation

    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 ...

  8. Gillespie algorithm - Wikipedia

    en.wikipedia.org/wiki/Gillespie_algorithm

    The process that led to the algorithm recognizes several important steps. In 1931, Andrei Kolmogorov introduced the differential equations corresponding to the time-evolution of stochastic processes that proceed by jumps, today known as Kolmogorov equations (Markov jump process) (a simplified version is known as master equation in the natural sciences).

  9. Stochastic simulation - Wikipedia

    en.wikipedia.org/wiki/Stochastic_simulation

    ResAssure - Stochastic reservoir simulation software - solves fully implicit, dynamic three-phase fluid flow equations for every geological realisation. Cain - Stochastic simulation of chemical kinetics. Direct, next reaction, tau-leaping, hybrid, etc. pSSAlib - C++ implementations of all partial-propensity methods. StochPy - Stochastic ...