Brownian motion definition

Brownian motion originally means the random motion of small particles suspended in fluids. It was named for the botanist R. Brown, the first to study such phenomena (1827). In 1905, Einstein made its statistical analysis, and observed that the probabilistic behavior of particles is described by the heat equation (Remark 17.2 (2)).
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Examples of Brownian motion in a sentence

  • Motivated by an attempt to model the fluctuations of asset prices, Brownian motion (i.e., the continuous-time random walk process [▇▇▇▇▇▇ 2004]) was first introduced by ▇▇▇▇▇▇▇▇▇ [1900] to price an option.

  • Therefore the intensity of fluctuations in scattered light (due to Brownian motion of particles in solution) are analysed by an autocorrelation method to yield a diffusion constant and ultimately a particle size expressed as the mean hydrodynamic diameter (▇▇▇▇, S.T. et al., 1994).

  • Therefore, in the absence of CICR, computationally inexpensive simulations of Markovian stochastic channel gating can be combined with deterministic models of Ca2+ diffusion and binding (either compartment-based or spatially resolved), leading to computationally inexpensive methods that avoid simulations of particle-based Brownian motion and stochastic reactions [7, 27-30].

  • In the GBM model, the proportional price changes are exponentially generated by a Brownian motion.

  • Systolic and hyper-systolic algorithms for the gravitational N-body problem, with an application to Brownian motion.

  • Sixty five years later, ▇▇▇▇▇▇▇▇▇ [1965] replaced ▇▇▇▇▇▇▇▇▇’▇ assumptions on asset price with a geometric form, called the geo- metric Brownian motion (GBM).

  • Its movement can be de- scribed by a multivariate geometric Brownian motion (GBM) [▇▇▇▇▇▇▇▇▇ 1965]: dCi(t) = µiCi(t)dt + σiCi(t)dWi(t), i = 1, .

  • The Variance-Gamma Lévy process is a pure jump and infinite activity Lévy process which can be understood as an extension of the Brownian motion which its drift subjected to random time changes under a gamma process, see ▇▇▇▇▇ and ▇▇▇▇▇▇ (1990) and ▇▇▇▇▇▇ (2007), among others, for more details.

  • Excess heat increases the Brownian motion and could result in microcoagulum and coagulum due to particle agglomeration.

  • A firm has assets-in-place that generate operating cash flow at the rate of Yt, which is publicly observable and for t ě 0, evolves according to dYt = µ(Yt)dt ` ν(Yt)dZt ` ζ(Yt−)dNt, (2) where µ(Yt) and ν(Yt) are general functions that satisfy the standard regularity conditions; tZtutě0 is a Brownian motion; tNtutě0 is a Poisson process with intensity λ(Yt) ą 0; and ζ(Yt−) is the jump size given the Poisson event.

Related to Brownian motion

  • DIP Motion means a motion to be filed by the Debtors with the Bankruptcy Court seeking Bankruptcy Court approval of the DIP Facility, which motion shall be consistent in all material respects with this Agreement and otherwise in form and substance reasonably acceptable to the Requisite Parties.

  • Sale Motion means the motion or motions of Sellers filed with the Bankruptcy Court seeking approval and entry of the Sale Order.

  • EUMA means the “SAP Delivered Support Agreement” which sets out the terms and conditions under which SAP provides support to End Users and which will be provided by SAP on a deal by deal basis.

  • SITC means the Standard International Trade Classification, Revision 3 (SITC, Rev. 3), published by the United Nations in Statistical Papers, Series M, No. 34/Rev. 3 (1986);

  • Civil action means all suits or claims of a civil nature in a state or federal court, whether cognizable as cases at law or in equity or admiralty. "Civil action" does not include any of the following: