Abstract The present study addresses the sensitivity analysis of particle concentration dispersion in the turbulent flow. A stochastic spectral model of turbulence is used to simulate the particle transfer. Sensitivity analysis is performed by estimations of Morris and Sobol indices. This study allows to define the significant and nonsignificant model parameters. It also gives an idea of the qualitative behavior of the stochastic model used.
{"title":"Sensitivity analysis of the concentration transport estimation in a turbulent flow","authors":"D. Kolyukhin, K. Sabelfeld, I. Dimov","doi":"10.1515/mcma-2022-2116","DOIUrl":"https://doi.org/10.1515/mcma-2022-2116","url":null,"abstract":"Abstract The present study addresses the sensitivity analysis of particle concentration dispersion in the turbulent flow. A stochastic spectral model of turbulence is used to simulate the particle transfer. Sensitivity analysis is performed by estimations of Morris and Sobol indices. This study allows to define the significant and nonsignificant model parameters. It also gives an idea of the qualitative behavior of the stochastic model used.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"211 - 219"},"PeriodicalIF":0.9,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41380538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The simulated annealing (SA) algorithm is a popular intelligent optimization algorithm which has been successfully applied in many fields. In this paper, we propose a software component under the Windows environment called goRDS which implements a refined descriptive sampling (RDS) number generator of high quality in the MATLAB programming language. The aim of this generator is to sample random inputs through the RDS method to be used in the Simple SA algorithm with swap operator. In this way, the new probabilistic meta-heuristic algorithm called RDS-SA algorithm will enhance the simple SA algorithm with swap operator, the SA algorithm and possibly its variants with solutions of better quality and precision. Towards this goal, the goRDS generator was highly tested by adequate statistical tests and compared statistically to the random number generator (RNG) of MATLAB, and it was proved that goRDS has passed all tests better. Simulation experiments were carried out on the benchmark traveling salesman problem (TSP) and the results show that the solutions obtained with the RDS-SA algorithm are of better quality and precision than those of the simple SA algorithm with swap operator, since the software component goRDS represents the probability behavior of the SA input random variables better than the usual RNG.
{"title":"Refined descriptive sampling simulated annealing algorithm for solving the traveling salesman problem","authors":"Meriem Cherabli, Megdouda Ourbih-Tari, Meriem Boubalou","doi":"10.1515/mcma-2022-2113","DOIUrl":"https://doi.org/10.1515/mcma-2022-2113","url":null,"abstract":"Abstract The simulated annealing (SA) algorithm is a popular intelligent optimization algorithm which has been successfully applied in many fields. In this paper, we propose a software component under the Windows environment called goRDS which implements a refined descriptive sampling (RDS) number generator of high quality in the MATLAB programming language. The aim of this generator is to sample random inputs through the RDS method to be used in the Simple SA algorithm with swap operator. In this way, the new probabilistic meta-heuristic algorithm called RDS-SA algorithm will enhance the simple SA algorithm with swap operator, the SA algorithm and possibly its variants with solutions of better quality and precision. Towards this goal, the goRDS generator was highly tested by adequate statistical tests and compared statistically to the random number generator (RNG) of MATLAB, and it was proved that goRDS has passed all tests better. Simulation experiments were carried out on the benchmark traveling salesman problem (TSP) and the results show that the solutions obtained with the RDS-SA algorithm are of better quality and precision than those of the simple SA algorithm with swap operator, since the software component goRDS represents the probability behavior of the SA input random variables better than the usual RNG.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"175 - 188"},"PeriodicalIF":0.9,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48841357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Randomized scalable vector algorithms for calculation of matrix iterations and solving extremely large linear algebraic equations are developed. Among applications presented in this paper are randomized iterative methods for large linear systems of algebraic equations governed by M-matrices. The crucial idea of the randomized method is that the iterations are performed by sampling random columns only, thus avoiding not only matrix-matrix but also matrix-vector multiplications. The suggested vector randomized methods are highly efficient for solving linear equations of high dimension, the computational cost depends only linearly on the dimension.
{"title":"Randomized Monte Carlo algorithms for matrix iterations and solving large systems of linear equations","authors":"K. Sabelfeld","doi":"10.1515/mcma-2022-2114","DOIUrl":"https://doi.org/10.1515/mcma-2022-2114","url":null,"abstract":"Abstract Randomized scalable vector algorithms for calculation of matrix iterations and solving extremely large linear algebraic equations are developed. Among applications presented in this paper are randomized iterative methods for large linear systems of algebraic equations governed by M-matrices. The crucial idea of the randomized method is that the iterations are performed by sampling random columns only, thus avoiding not only matrix-matrix but also matrix-vector multiplications. The suggested vector randomized methods are highly efficient for solving linear equations of high dimension, the computational cost depends only linearly on the dimension.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"125 - 133"},"PeriodicalIF":0.9,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44607622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We study the convergence of Langevin-simulated annealing type algorithms with multiplicative noise, i.e. for V : R d → R Vcolonmathbb{R}^{d}tomathbb{R} a potential function to minimize, we consider the stochastic differential equation d Y t = − σ σ ⊤ ∇ V ( Y t ) d t + a ( t ) σ ( Y t ) d W t + a ( t ) 2 Υ ( Y t ) d t dY_{t}=-sigmasigma^{top}nabla V(Y_{t}),dt+a(t)sigma(Y_{t}),dW_{t}+a(t)^{2}Upsilon(Y_{t}),dt , where ( W t ) (W_{t}) is a Brownian motion, σ : R d → M d ( R ) sigmacolonmathbb{R}^{d}tomathcal{M}_{d}(mathbb{R}) is an adaptive (multiplicative) noise, a : R + → R + acolonmathbb{R}^{+}tomathbb{R}^{+} is a function decreasing to 0 and where Υ is a correction term. Allowing 𝜎 to depend on the position brings faster convergence in comparison with the classical Langevin equation d Y t = − ∇ V ( Y t ) d t + σ d W t dY_{t}=-nabla V(Y_{t}),dt+sigma,dW_{t} . In a previous paper, we established the convergence in L 1 L^{1} -Wasserstein distance of Y t Y_{t} and of its associated Euler scheme Y ¯ t bar{Y}_{t} to argmin ( V ) operatorname{argmin}(V) with the classical schedule a ( t ) = A log − 1 / 2 ( t ) a(t)=Alog^{-1/2}(t) . In the present paper, we prove the convergence in total variation distance. The total variation case appears more demanding to deal with and requires regularization lemmas.
研究了具有乘性噪声的langevin模拟退火算法的收敛性，即对于V:R d→R V colonmathbb{R} ^{d}tomathbb{R}一个最小化的势函数，我们考虑随机微分方程d²Y t=- σ∑∑∞∞∞V(Y t)∑d∑t+a∑(t)∑∑(Y t)∑d∑W t+a∑(t)²∑(t)²{dY＿t}=- sigmasigma{top}nabla V{(Y＿t)}，dt+a(t)²sigma (Y＿t){，}dW＿t{+a(t)}²{}Upsilon (Y＿t){，dt，其中(W t) }(W＿t){是布朗运动，σ:R d→M d²(R) }sigmacolonmathbb{R} ^{d}tomathcal{M} ＿d{(}mathbb{R})是一个自适应(乘性)噪声，a: R +→R + a colonmathbb{R} ^{+}tomathbb{R} ^{+}是一个递减到0的函数，其中Υ是一个校正项。与经典朗之万方程d¹Y t=-∇V∑(Y t)∑d∑W t dY＿t=- {}nabla V{(Y＿t)}，dt+ sigma ，{dW＿t}相比，允许其依赖于位置带来了更快的收敛速度。在上一篇文章中，我们建立了在l1l ^{1} -Wasserstein距离下，Y t {Y＿t}及其相关的欧拉格式Y¯t bar{Y} ＿t{到argmin (V) }operatorname{argmin} (V)的收敛性，其经典调度为a¹(t)= a²log -1/2(t) a(t)= a log ^{-1/2}(t)。本文证明了该算法在总变差距离上的收敛性。全变分情况的处理难度更大，需要正则化引理。
{"title":"Convergence of Langevin-simulated annealing algorithms with multiplicative noise II: Total variation","authors":"Pierre Bras, G. Pagès","doi":"10.1515/mcma-2023-2009","DOIUrl":"https://doi.org/10.1515/mcma-2023-2009","url":null,"abstract":"Abstract We study the convergence of Langevin-simulated annealing type algorithms with multiplicative noise, i.e. for V : R d → R Vcolonmathbb{R}^{d}tomathbb{R} a potential function to minimize, we consider the stochastic differential equation d Y t = − σ σ ⊤ ∇ V ( Y t ) d t + a ( t ) σ ( Y t ) d W t + a ( t ) 2 Υ ( Y t ) d t dY_{t}=-sigmasigma^{top}nabla V(Y_{t}),dt+a(t)sigma(Y_{t}),dW_{t}+a(t)^{2}Upsilon(Y_{t}),dt , where ( W t ) (W_{t}) is a Brownian motion, σ : R d → M d ( R ) sigmacolonmathbb{R}^{d}tomathcal{M}_{d}(mathbb{R}) is an adaptive (multiplicative) noise, a : R + → R + acolonmathbb{R}^{+}tomathbb{R}^{+} is a function decreasing to 0 and where Υ is a correction term. Allowing 𝜎 to depend on the position brings faster convergence in comparison with the classical Langevin equation d Y t = − ∇ V ( Y t ) d t + σ d W t dY_{t}=-nabla V(Y_{t}),dt+sigma,dW_{t} . In a previous paper, we established the convergence in L 1 L^{1} -Wasserstein distance of Y t Y_{t} and of its associated Euler scheme Y ¯ t bar{Y}_{t} to argmin ( V ) operatorname{argmin}(V) with the classical schedule a ( t ) = A log − 1 / 2 ( t ) a(t)=Alog^{-1/2}(t) . In the present paper, we prove the convergence in total variation distance. The total variation case appears more demanding to deal with and requires regularization lemmas.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"29 1","pages":"203 - 219"},"PeriodicalIF":0.9,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45446788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper is devoted to one possible way of the model construction for the stationary Gaussian process with given accuracy and reliability in functional space C ( [ 0 , T ] ) {C([0,T])} .
摘要本文致力于在函数空间C（[0，T]）{C（[0]，T]。
{"title":"On one way of modeling a stochastic process with given accuracy and reliability","authors":"T. Ianevych, I. Rozora, A. Pashko","doi":"10.1515/mcma-2022-2110","DOIUrl":"https://doi.org/10.1515/mcma-2022-2110","url":null,"abstract":"Abstract The paper is devoted to one possible way of the model construction for the stationary Gaussian process with given accuracy and reliability in functional space C ( [ 0 , T ] ) {C([0,T])} .","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"135 - 147"},"PeriodicalIF":0.9,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48045457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The Black–Karasinski model is a one-factor non-affine interest rate model as it describes interest rate movements driven by a single source of randomness and the drift function is a nonlinear function of the interest rate. The drift parameters represent the level and the speed of mean reversion of the interest rate. It belongs to the class of no-arbitrage models. The paper introduces some new approximate minimum contrast estimators of the mean reversion speed parameter in the model based on discretely sampled data which are efficient and studies their asymptotic distributional properties with precise rates of convergence.
{"title":"Berry–Esseen inequalities for the fractional Black–Karasinski model of term structure of interest rates","authors":"J. Bishwal","doi":"10.1515/mcma-2022-2111","DOIUrl":"https://doi.org/10.1515/mcma-2022-2111","url":null,"abstract":"Abstract The Black–Karasinski model is a one-factor non-affine interest rate model as it describes interest rate movements driven by a single source of randomness and the drift function is a nonlinear function of the interest rate. The drift parameters represent the level and the speed of mean reversion of the interest rate. It belongs to the class of no-arbitrage models. The paper introduces some new approximate minimum contrast estimators of the mean reversion speed parameter in the model based on discretely sampled data which are efficient and studies their asymptotic distributional properties with precise rates of convergence.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"111 - 124"},"PeriodicalIF":0.9,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42953837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We address the problem of statistical simulation of a scalar real Gaussian random field inside the unit 3D ball. Two different methods are studied: (i) the method based on the known homogeneous isotropic power spectrum developed by Meschede and Romanowicz [M. Meschede and B. Romanowicz, Non-stationary spherical random media and their effect on long-period mantle waves, Geophys. J. Int. 203 2015, 1605–1625] and (ii) the method based on known radial and angular covariance functions suggested in this work. The first approach allows the extension of the simulation technique to the inhomogeneous or anisotropic case. However, the disadvantage of this approach is the lack of accurate statistical characterization of the results. The accuracy of considered methods is illustrated by numerical tests, including a comparison of the estimated and analytical covariance functions. These methods can be used in many applications in geophysics, geodynamics, or planetary science where the objective is to construct spatial realizations of 3D random fields based on a statistical analysis of observations collected on the sphere or within a spherical region.
{"title":"Simulation of Gaussian random field in a ball","authors":"D. Kolyukhin, A. Minakov","doi":"10.1515/mcma-2022-2108","DOIUrl":"https://doi.org/10.1515/mcma-2022-2108","url":null,"abstract":"Abstract We address the problem of statistical simulation of a scalar real Gaussian random field inside the unit 3D ball. Two different methods are studied: (i) the method based on the known homogeneous isotropic power spectrum developed by Meschede and Romanowicz [M. Meschede and B. Romanowicz, Non-stationary spherical random media and their effect on long-period mantle waves, Geophys. J. Int. 203 2015, 1605–1625] and (ii) the method based on known radial and angular covariance functions suggested in this work. The first approach allows the extension of the simulation technique to the inhomogeneous or anisotropic case. However, the disadvantage of this approach is the lack of accurate statistical characterization of the results. The accuracy of considered methods is illustrated by numerical tests, including a comparison of the estimated and analytical covariance functions. These methods can be used in many applications in geophysics, geodynamics, or planetary science where the objective is to construct spatial realizations of 3D random fields based on a statistical analysis of observations collected on the sphere or within a spherical region.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"85 - 95"},"PeriodicalIF":0.9,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49609752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper introduces a novel high order discretization scheme for expectation of jump-diffusion processes by using a Malliavin calculus approach and an operator splitting method. The test function of the target expectation is assumed to be only Lipschitz continuous in order to apply the method to financial problems. Then Kusuoka’s estimate is employed to justify the proposed discretization scheme. The algorithm with a numerical example is shown for implementation.
{"title":"A high order weak approximation for jump-diffusions using Malliavin calculus and operator splitting","authors":"Naho Akiyama, Toshihiro Yamada","doi":"10.1515/mcma-2022-2109","DOIUrl":"https://doi.org/10.1515/mcma-2022-2109","url":null,"abstract":"Abstract The paper introduces a novel high order discretization scheme for expectation of jump-diffusion processes by using a Malliavin calculus approach and an operator splitting method. The test function of the target expectation is assumed to be only Lipschitz continuous in order to apply the method to financial problems. Then Kusuoka’s estimate is employed to justify the proposed discretization scheme. The algorithm with a numerical example is shown for implementation.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"97 - 110"},"PeriodicalIF":0.9,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44300277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we propose a recursive estimators of the regression function based on the two-time-scale stochastic approximation algorithms and the Bernstein polynomials. We study the asymptotic properties of this estimators. We compare the proposed estimators with the classic regression estimator using the Bernstein polynomial defined by Tenbusch. Results showed that, our proposed recursive estimators can overcome the problem of the edges associated with kernel regression estimation with a compact support. The proposed recursive two-time-scale estimators are compared to the non-recursive estimator introduced by Tenbusch and the performance of the two estimators are illustrated via simulations as well as two real datasets.
{"title":"Recursive regression estimation based on the two-time-scale stochastic approximation method and Bernstein polynomials","authors":"Y. Slaoui, Salima Helali","doi":"10.1515/mcma-2022-2104","DOIUrl":"https://doi.org/10.1515/mcma-2022-2104","url":null,"abstract":"Abstract In this paper, we propose a recursive estimators of the regression function based on the two-time-scale stochastic approximation algorithms and the Bernstein polynomials. We study the asymptotic properties of this estimators. We compare the proposed estimators with the classic regression estimator using the Bernstein polynomial defined by Tenbusch. Results showed that, our proposed recursive estimators can overcome the problem of the edges associated with kernel regression estimation with a compact support. The proposed recursive two-time-scale estimators are compared to the non-recursive estimator introduced by Tenbusch and the performance of the two estimators are illustrated via simulations as well as two real datasets.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"45 - 59"},"PeriodicalIF":0.9,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44769876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper considers integral approximation via importance sampling where the importance sampler is chosen from a family of skew-Student distributions. This is an alternative class of distributions than is typically considered in importance sampling applications. We describe variate generation and propose adaptive methods for fitting a member of the skew-Student family to a particular integral. We also demonstrate the utility of the approach in several examples.
{"title":"Moment matching adaptive importance sampling with skew-student proposals","authors":"Shijia Wang, T. Swartz","doi":"10.1515/mcma-2022-2106","DOIUrl":"https://doi.org/10.1515/mcma-2022-2106","url":null,"abstract":"Abstract This paper considers integral approximation via importance sampling where the importance sampler is chosen from a family of skew-Student distributions. This is an alternative class of distributions than is typically considered in importance sampling applications. We describe variate generation and propose adaptive methods for fitting a member of the skew-Student family to a particular integral. We also demonstrate the utility of the approach in several examples.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"268 1‐2","pages":"149 - 162"},"PeriodicalIF":0.9,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41262953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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