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Regression-Based Variance Reduction Approach for Strong Approximation Schemes
P. 131–178.
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the terminal functionals. In this way the complexity order of the standard Monte Carlo algorithm (ε−3) can be reduced down to ε−2 log(ε−1) in case of the Euler scheme with ε being the precision to be achieved. These theoretical results are illustrated by several numerical examples.
Publication based on the results of:
In book
Heidelberg: Springer, 2017.
A. A. Ponomarev, N. L. Aleksandrov, Plasma Physics Reports 2026 Vol. 52 No. 3 P. 367–378
An approximate method for calculating drift velocity and other kinetic coefficients of heavy ions
in a light gas is generalized to gaseous mixtures. Obtained equations are used to calculate the mobilities of
and ions, as well as rate constants for inelastic ion–molecule processes with these ions in helium with
small additions of O2 under an electric field. Calculated ...
Added: April 27, 2026
Tsvetkova O., Ouarda T., Journal of Renewable and Sustainable Energy 2019 Vol. 11 No. 5 P. 053303–053303
The present paper bridges mathematical modeling and wind resource assessment (WRA). Sensitivity analysis (SA) links portions of output variance to the variance in each input variable. Global SA (GSA) explores inputs globally. One-at-a-time SA is dominating in WRA, while GSA is often overlooked. Compared to traditional methods, GSA offers potential improvement by the means of ...
Added: September 15, 2025
Aleksandrov N., Ponomarev A., Plasma Physics Reports 2024 Vol. 50 No. 12 P. 1577–1584
Using an approximate approach that is valid for a large ratio of the ion mass to the mass of the neutral
particle, the mobility of O2+, N2+, O2-, and O4- ions was calculated in helium and good agreement was
obtained with the available results of Monte Carlo calculations and experimental data at high values of the
reduced electric ...
Added: March 25, 2025
Weigel M., Barash L., Shchur L. et al., / Series cond-mat "arxiv.org". 2021. No. 2102.06611.
Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest caliber. Here we study ...
Added: February 15, 2021
Russkov A., Chulkevich R., Shchur L., Computer Physics Communications 2021 Vol. 261 P. 107786
The population annealing method is a promising approach for large-scale simulations because it is potentially scalable on any parallel architecture. We present an implementation of the algorithm on a hybrid program architecture combining CUDA and MPI. The problem is to keep all general-purpose graphics processing unit devices as busy as possible by efficiently redistributing replicas. ...
Added: December 28, 2020
Romanyuk K., Ichkitidze Y., , in: Intelligent Computing: Proceedings of the 2020 Computing Conference, Volume 1. Advances in Intelligent Systems and ComputingVol. 1228.: Springer, 2020. P. 281–286.
Credit rating agencies evaluate corporate risks and assign ratings to companies. Each rating grade corresponds to certain boundaries of default probability. KMV is a popular model to assess the default probability of a company. In this paper, a method to predict the default probability of a company is proposed. This method is based on the ...
Added: November 28, 2020
Makarova V. A., Dalal A., , in: III International Science Conference SER 2020. New Trends and Best Practices in Socioeconomic Research.: Podgorica: Economic Laboratory for Transition Research, Podgorica, Montenegro, 2020. P. 54–55.
The study considers corporate inversion, also known as tax inversion, which involves companies to move their operations overseas in order to avoid tax burden in the domestic country. Although the following strategy gains popularity among corporate managers, experts emphasize its’ controversial and risky nature (Lusch et al., 2016). The aim of this paper is twofold. First, we ...
Added: November 1, 2020
Chaudru de Raynal P., Menozzi S., / Series arXiv "math". 2019.
We establish well-posedness results for multidimensional non degenerate α-stable driven SDEs with time inhomogeneous singular drifts in Lr−B−1+γp,q with γ<1 and α in (1,2], where Lr and B−1+γp,q stand for Lebesgue and Besov spaces respectively. Precisely, we first prove the well-posedness of the corresponding martingale problem and then give a precise meaning to the dynamics of the SDE. Our results rely on the smoothing properties of the ...
Added: October 31, 2020
Belomestny D., Schoenmakers J., SIAM Journal on Control and Optimization 2020 Vol. 58 No. 1 P. 529–550
In this paper we study optimal stopping problems for nonlinear Markov processes driven by a McKean-Vlasov SDE and aim at solving them numerically by Monte Carlo. To this end we propose a novel regression algorithm based on the corresponding particle system and prove its convergence. The proof of convergence is based on perturbation analysis of ...
Added: May 8, 2020
Shchur L., Journal of Physics: Conference Series 2019 Vol. 1252 P. 012010-1–012010-7
We review recent advances in the analysis of the Wang–Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random ...
Added: August 22, 2019
Efremov R., Journal of Chemical Information and Modeling 2019 Vol. 59 No. 6 P. 2765–2775
Atomistic aspects of the structural organization, dynamics, and functioning of hydrated lipid bilayers - model cell membranes - are primarily governed by the fine balance of intermolecular interactions between all constituents of these systems. Besides the hydrophobic effect, which shapes the overall skeleton of lipid membranes, very important contribution to their behavior is made by ...
Added: August 7, 2019
Shchur L., / Series arXiv "math". 2018. No. 1808.09251.
We review recent advances in the analysis of the Wang--Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random ...
Added: August 29, 2018
Bondarenko S., Сапронов А. А., Computer Physics Communications 2013 No. 184 P. 2343–2350
mcsanc is a Monte-Carlo tool based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules for higher order calculations in hadron collider physics. It allows to evaluate NLO QCD and EW cross sections for Drell-Yan processes (inclusive), associated Higgs and gauge boson production and single-top quark production in s- and ...
Added: June 27, 2018
Romanyuk K., , in: Proceedings of the 2016 Future Technologies Conference.: IEEE, 2017. P. 254–259.
In the given paper the aggregated randomized indices method is modified for credit scoring. Coefficients of the modified method can be calibrated on a massive training set in comparison with a standard version. Different credit scoring models are analyzed, i.e. with a binary scale and a continuous one. The Monte Carlo method is applied to ...
Added: November 20, 2017
Barash L. Yu., Weigel M., Shchur L.N. et al., European Physical Journal: Special Topics 2017 Vol. 226 No. 4 P. 595–604
Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the problems in computational physics that are difficult to tackle with standard methods such as local-update simulations in the canonical ensemble, for example ...
Added: October 20, 2017
Barash L. Yu., M. A. Fadeeva, Shchur L. N., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 96 No. 4 Article 043307
The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of ...
Added: October 20, 2017
Konakov V., Markova A., Automation and Remote Control 2017 Vol. 78 No. 8 P. 1438–1448
We consider the diffusion process and its approximation by Markov chain with nonlinear unbounded trends. The usual parametrix method is not applicable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear unbounded trend and move to stochastic differential equation with bounded drift and diffusion coefficients. A similar procedure is ...
Added: August 28, 2017
Barash L., Guskova M. S., Shchur L., Programming and Computer Software 2017 Vol. 43 No. 3 P. 145–160
By the example of the RNGAVXLIB random number generator library, this paper considers some approaches to employing AVX vectorization for calculation speedup. The RNGAVXLIB library contains AVX implementations of modern generators and the routines allowing one to initialize up to 10^19 independent ran-dom number streams. The AVX implementations yield exactly the same pseudorandom sequences as ...
Added: March 24, 2017
Gostev I. M., Gevorkyan M., Hnatich M. et al., , in: Distributed Computer and Communication Networks 19th International Conference, DCCN 2016, Moscow, Russia, November 21-25, 2016, Revised Selected PapersVol. 678.: Wien: Springer, 2016. P. 538–552.
This paper studies program implementation problem of pseudo-random number generators in OpenModelica. We give an overview of generators of pseudo-random uniform distributed numbers. They are used as a basis for construction of generators of normal and Poisson distributions. The last step is the creation of Wiener and Poisson stochastic processes generators. We also describe the ...
Added: February 19, 2017