97 research outputs found
Quasi-Two-Dimensional Dynamics of Plasmas and Fluids
In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente
Strong Approximation of Empirical Copula Processes by Gaussian Processes
We provide the strong approximation of empirical copula processes by a
Gaussian process. In addition we establish a strong approximation of the
smoothed empirical copula processes and a law of iterated logarithm
Extremes of threshold-dependent Gaussian processes
In this contribution we are concerned with the asymptotic behaviour, as u→∞, of P{supt∈[0,T]Xu(t)>u}, where Xu(t),t∈[0,T],u>0 is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns P{supt∈[0,T](X(t)+g(t))>u}, as u→∞, for X a centered Gaussian process and g some measurable trend function. Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest
Gaussian risk models with financial constraints
In this paper, we investigate Gaussian risk models which include financial elements, such as inflation and interest rates. For some general models for inflation and interest rates, we obtain an asymptotic expansion of the finite-time ruin probability for Gaussian risk models. Furthermore, we derive an approximation of the conditional ruin time by an exponential random variable as the initial capital tends to infinity
Parisian ruin over a finite-time horizon
For a risk process , where is the initial
capital, is the premium rate and is an aggregate claim
process, we investigate the probability of the Parisian ruin with a given positive constant and a positive measurable
function . We derive asymptotic expansion of , as
, for the aggregate claim process modeled by Gaussian
processes. As a by-product, we derive the exact tail asymptotics of the infimum
of a standard Brownian motion with drift over a finite-time interval.Comment: 2
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