We extend the general framework of the Multilevel Monte Carlo method to multilevel estimation of arbitrary order central statistical moments. In particular, we prove that under certain assumptions, the total cost of a MLMC central moment estimator is asymptotically the same as the cost of the multilevel sample mean estimator and thereby is asymptotically the same as the cost of a single determi...

We present an r -adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical c...

This research proposes that, in cases where threshold covariates are either unavailable or difficult to observe, practitioners should treat these characteristics as latent, and use simulated maximum likelihood techniques to control for them. Two econometric frameworks for doing so in a more flexible manner are proposed. The finite sample performance of these new specifications are investigated ...

In this manuscript, we establish an integration by parts formula for the quadrature of discontinuous payoffs in a multidimensional Heston model. For its derivation we use Malliavin calculus techniques and work under mild integrability conditions on the payoff and under the assumption of a strictly positive volatility. Since the integration by parts procedure smoothes the original functional, ou...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

The problen of the backscattering of electrons from metal targets is subject of extensive theoreticel and experimental work in surface analysis. We are interested in the angular distribution of the backscattered electrons. The flow of electrons satisfies an integral equation, which might be solved by Monte Carlo methods. The Monte Carlo approach, used by A.Dubus, A. Jablonski and S.Tougaard in ...

Results of numerical modeling of dilute 2D and 3D crystalline lattices are presented. The percolation thresholds for face-centered cubic (fcc), body-centered cubic (bcc) and the simple cubic (sc) lattices for the first, second and third coordination spheres are obtained by means of Monte Carlo (MC) method. It is shown, that the mean value of the percolation cluster density has a minimum value a...

Researchers modeling the behavior of individual people or firms are often unable to utilize microlevel data because such data are unavailable or unreliable. Faced with this dilemma, researchers often resort to using aggregate-level data. When the individual-level variable of interest is dichotomous, however, the aggregate-level model is subject to a special form of aggregation bias. Kelejian [1...

For a d-dimensional quasi-Monte Carlo method with n points, calculating the weighted L 2 discrepancy using a formula obtained directly from its deenition requires O(2 d?1 dn 2) operations. Here we give an alternative formula requiring O(dn 2) operations. We also present the rst numerical calculations of the weighted L 2 discrepancy. These results give supporting evidence for thèlimiting discrep...

We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The lgorithm uses iteratively the idea of separating the domain of integration into 2subregions. The proposed algorithm can be applied irectly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional ntegral...