Article
Stratified regression-based variance reduction approach for weak approximation schemes
In this paper we suggest a modification of the regression-based variance reduction approach recently proposed in Belomestny et al. This modification is based on the stratification technique and allows for a further significant variance reduction. The performance of the proposed approach is illustrated by several numerical examples.
The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next-nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin-spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization-group calculations.
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in case where the random walk terminates at some boundary. We recently found that a finite step of the random walk produces a bias in the hitting probability and this bias vanishes in the limit of an infinitesimal step. Therefore, it is important to know how a change in the step size of the random walk influences the performance of simulations. We propose an algorithm with the most effective procedure for the step-length-change protocol.
Risk Management approach is an essential part of the project. Large industries and particular companies incorporate RM Culture. Statistics shows, that companies with Project Management (PM) Structure reduce cost ineffectiveness up to 20%. In oil and gas industry PM Risk Analysis (PRMA) has been widely used for the last years. Various models and procedures have been developed to manage projects of different scale. Nonetheless, Offshore Projects (OP) complexity, high uncertainty of technical, financial, market and government factors, as well as different sea conditions, still makes sense to improve general PRMA models according to the oil and gas OP features. Traditional RM tools and techniques are not appropriate to cope with complex projects in the Arctic. Companies will have to modify risk assessment process or look for new methods. The paper suggests OPRMM, where the attempt to implement PM tools and techniques together with mathematical modeling and expert assessment is made and institutional factors are included. Practically, it is founded on the comparison between offshore field development in the Barents Sea and the Kara Sea. The reason for research is debates around future Arctic oil and gas projects and their commercial potential. Several large projects with participation of major international companies in the Barents Sea and the prospectivity of the Kara Sea Projects in conditions of technology difficulties are under discussion and have not reached the investment project phase yet. OPRMM starts with identifying the key factors, which could affect offshore field development. Inside the investment regime modified real option value (ROV) model for OP is developed: stop option and scale transformation option. Basing on the binominal trees and Monte Carlo Simulation it is possible to see the perspectives of the OP at an early stage in the conditions of high uncertainty. Incorporating the ROV model into investment regime allows operator to choose the territory to explore. The research shows, that offshore projects in the Arctic offshore is not only under the pressure of internal corporative factors, but also under influence of external institutional factors. New tools and approaches will be required in Arctic projects where no one wants to be looking in the wrong place.
We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the three- and four-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traffic is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the final node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a finite-dimensional system of differential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of differential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.