Published by De Gruyter

Volume 22 Issue 1

Issue of Monte Carlo Methods and Applications

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Contents
Journal Overview

Publicly Available March 1, 2016

Frontmatter

Page range: i-iv

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February 17, 2016

An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers

David Dereudre, Sara Mazzonetto, Sylvie Roelly

Page range: 1-23

Abstract

In this paper, we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover, we propose a rejection sampling method to simulate this density in an exact way.

February 17, 2016

Special quasirandom structures: A selection approach for stochastic homogenization

Claude Le Bris, Frédéric Legoll, William Minvielle

Page range: 25-54

Abstract

We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [23], [24], [25], consists in selecting random realizations that best satisfy some statistical properties (such as the volume fraction of each phase in a composite material) usually only obtained asymptotically. We study the approach theoretically in some simplified settings (one-dimensional setting, perturbative setting in higher dimensions), and numerically demonstrate its efficiency in more general cases.

March 2, 2016

Splitting and survival probabilities in stochastic random walk methods and applications

Karl K. Sabelfeld

Page range: 55-72

Abstract

We suggest a series of extremely fast stochastic algorithms based on exact representations we derive in this paper for the first passage time and exit point probability densities, splitting and survival probabilities. We apply the developed algorithms to the following three classes of problems: (1) simulation of epitaxial nanowire growth, (2) diffusion imaging of microstructures, in particular, cathodoluminescence imaging for threading dislocations, and (3) simulation of the annihilation of electrons and holes in vicinity of nonradiative centers and quantum efficiency evaluation. In the last example the Random Walk on Spheres method is used to solve nonlinear diffusion equations, and to more general systems of nonlinear Smoluchowski equations combined with the kinetic Monte Carlo method.

February 17, 2016

The Manhattan Project, the first electronic computer and the Monte Carlo method

Dobriyan M. Benov

Page range: 73-79

Abstract

The background of the Monte Carlo method is connected with two very important events in the modern human history: the World War Two and the building of first electronic computers. For that reason, we will try to synthesize the most important facts of those events that have relation to the development of the method in order to produce a clearer picture of the origination of the Monte Carlo method of stochastic sampling. The research covers the period from 1930 to 1959.

About this journal

Objective
Monte Carlo Methods and Applications is a quarterly published journal that presents original articles on the theory and applications of Monte Carlo and Quasi-Monte Carlo methods. Launched in 1995 the journal covers all stochastic numerics topics with emphasis on the theory of Monte Carlo methods and new applications in all branches of science and technology. Stochastic models in all fields of applied sciences, in particular turbulence, rarefied gas dynamics and nanotechnology, bioscience, medicine, chemical kinetics and combustion, stochastic models in mathematical finance

Topics

Theory of Monte Carlo methods
Quasi-Monte Carlo methods
Integration
Boundary value problems for PDE's
Numerics of stochastic differential equations
Simulation of random variables, stochastic processes and fields

Article formats
Research articles

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