China
Africa
Explore chapters and articles related to this topic
Turbulence
Published in Wioletta Podgórska, Multiphase Particulate Systems in Turbulent Flows, 2019
As results from the works of Dubruelle (1994) and She and Waymire (1995), the local non-dimensional energy dissipation εl/εl∞ has a log-Poisson distribution. A variable with Poisson distribution is an example of an infinitely divisible random variable, i.e. a variable which can be written as a sum of an arbitrary number of independently and identically distributed variables. Poisson distribution occurs generally in connection with discontinuous random processes and is the natural limit of a wide class of statistical distributions involving rare events (Guikman and Skorokhod, 1969; Feller, 1971; Arratia et al., 1990; Dubruelle, 1994; Frisch, 1995). Dubruelle also noticed that the scaling properties of quantity εl∞ associated with the most intermittent dissipative structure can be presented more generally as εl∞~l−Δforl→0
Marginally and Conditionally Specified Multivariate Survival Models: A Survey
Published in Donald B. Owen, Subir Ghosh, William R. Schucany, William B. Smith, Statistics of Quality, 2020
i.e., any family of infinitely divisible distributions with support (0, ∞). We may readily define k-dimensional random vectors whose marginal distributions are in the family Fθ(z) by starting with l (usually ≥ k) independent random variables U1, …, Ut with FUi(u) = Fθi(u) and defining () Z=AU
Stabilisation of stochastic delayed systems with Lévy noise on networks via periodically intermittent control
Published in International Journal of Control, 2020
It has been presented that any Lévy process consists of two components: a Brownian motion and a Poisson random measure. The law of a Lévy process is infinitely divisible and its characteristic function is given by the –Khintchineformula: in which and are the mean and covariance of the Brownian motion , and is the intensity measure of Poisson random measure N. The triplet is the characteristic triplet of the Lévy process, which determines the characteristic function of , therefore it determines the laws of . A Lévy process is homogeneous if and only if its characteristic triplet is obtained by , where b and A are constants and λ is a Lévy measure satisfying . Several years ago a homogeneous Lévy process is simply called a Lévy process, see Kunita (2010).