A phenomenological two-fluid model of the (time-reversible) spectrally-truncated 3D Euler equation is proposed. The thermalized small scales are first shown to be quasi-normal. The effective viscosity and thermal diffusion are then determined, using EDQNM closure and Monte-Carlo numerical computations. Finally, the model is validated by comparing its dynamics with that of the original truncated...

We consider a modified version of the de Finetti model in insurance risk theory in which, when surpluses become negative the company has the possibility of borrowing, and thus continue its operation. For this model we examine the problem of estimating the “time-in-the red” over a finite horizon via simulation. We propose a smoothed estimator based on a conditioning argument which is very simple...

This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other numerical integrations for estimating conditional expec...

We continue the complexity analysis of parametric definite and indefinite integration given by the authors in [2]. Here we consider anisotropic classes of functions, including certain classes with dominating mixed derivatives. Our analysis is based on a multilevel Monte Carlo method developed in [2] and we obtain the order of the deterministic and randomized n-th minimal errors (in some limit c...

Average options are path-dependent and have payoffs which depend on the average price over a fixed period leading up to the maturity date. This option is of interest and important for thinly-traded assets since price manipulation is prohibited, and both the investor and issuer may enjoy a certain degree of protection from the caprice of the market. There are several nice results for the average...

In this paper, we use the lower record values from the inverse Weibull distribution (IWD) to develop and discuss different methods of estimation in two different cases, 1) when the shape parameter is known and 2) when both of the shape and scale parameters are unknown. First, we derive the best linear unbiased estimate (BLUE) of the scale parameter of the IWD. To compare the different methods o...

A novel and efficient quasi-Monte Carlo method for estimating the surface area of digitized 3D objects in the volumetric representation is presented. It operates directly on the original digitized objects without any surface reconstruction procedure. Based on the Cauchy–Crofton formula from integral geometry, the method estimates the surface area of a volumetric object by counting the number of...

where σ denotes the normalized surface measure on Sd and f is a continuous real valued function. As a general reference on Quasi-Monte Carlo methods we mention Niederreiter [22]. The problem of distributing points on the sphere is also related to constructive multivariate approximation, see Reimer [24]. For the recent literature on spherical problems concerned with approximation and numerical i...

This article presents differential equations and solution methods for the functions of the form A(z) = F−1(G(z)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of th...

The relative contribution to the radiometric force of the area and perimeter of the vane is studied experimentally and numerically. Experimentally, a circular vane, a low-aspect rectangular vane, and a high-aspect rectangular vane were all tested on a force balance, with nano-Newton resolution, placed in a stagnant gas. The computational results were obtained through 2-D simulations using the d...