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Monte Carlo Methods and Applications最新文献

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Statistical analysis of the estimates of some stationary performances of the unreliable M/M/1/N queue with Bernoulli feedback 具有伯努利反馈的不可靠M/M/1/N队列某些平稳性能估计的统计分析
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2023-05-03 DOI: 10.1515/mcma-2023-2004
Hadjer Nita, Fairouz Afroun, M. Cherfaoui, D. Aïssani
{"title":"Statistical analysis of the estimates of some stationary performances of the unreliable M/M/1/N queue with Bernoulli feedback","authors":"Hadjer Nita, Fairouz Afroun, M. Cherfaoui, D. Aïssani","doi":"10.1515/mcma-2023-2004","DOIUrl":"https://doi.org/10.1515/mcma-2023-2004","url":null,"abstract":"Abstract In this work, we considered the parametric estimation of the characteristics of the M / M / 1 / N {M/M/1/N} waiting model with Bernoulli feedback. Through a Monte-Carlo simulation study, we have illustrated the effect of the estimation of the starting parameters of the considered waiting system on the statistical properties of its performance measures estimates, when these latter are obtained using the plug-in method. In addition, several types of convergence (bias, variance, MSE, in law) of these performance measure estimators have also been showed by simulation.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"0 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41551785","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}
引用次数: 0
Computation of the steady-state probability of Markov chain evolving on a mixed state space 混合状态空间上马尔可夫链演化的稳态概率计算
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2023-03-30 DOI: 10.1515/mcma-2023-2003
Az-eddine Zakrad, A. Nasroallah
{"title":"Computation of the steady-state probability of Markov chain evolving on a mixed state space","authors":"Az-eddine Zakrad, A. Nasroallah","doi":"10.1515/mcma-2023-2003","DOIUrl":"https://doi.org/10.1515/mcma-2023-2003","url":null,"abstract":"Abstract The partitioning algorithm is an iterative procedure that computes explicitly the steady-state probability of a finite Markov chain 𝑋. In this paper, we propose to adapt this algorithm to the case where the state space E := C ∪ D E:=Ccup D is composed of a continuous part 𝐶 and a finite part 𝐷 such that C ∩ D = ∅ Ccap D=emptyset . In this case, the steady-state probability 𝜋 of 𝑋 is a convex combination of two steady-state probabilities π C pi_{C} and π D pi_{D} of two Markov chains on 𝐶 and 𝐷 respectively. The obtained algorithm allows to compute explicitly π D pi_{D} . If π C pi_{C} cannot be computed explicitly, our algorithm approximates it by numerical resolution of successive integral equations. Some numerical examples are studied to show the usefulness and proper functioning of our proposal.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43124785","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}
引用次数: 0
A time-step-robust algorithm to compute particle trajectories in 3-D unstructured meshes for Lagrangian stochastic methods 拉格朗日随机方法计算三维非结构化网格中粒子轨迹的时间步长鲁棒算法
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2023-03-15 DOI: 10.1515/mcma-2023-2002
Guilhem Balvet, J. Minier, C. Henry, Y. Roustan, M. Ferrand
{"title":"A time-step-robust algorithm to compute particle trajectories in 3-D unstructured meshes for Lagrangian stochastic methods","authors":"Guilhem Balvet, J. Minier, C. Henry, Y. Roustan, M. Ferrand","doi":"10.1515/mcma-2023-2002","DOIUrl":"https://doi.org/10.1515/mcma-2023-2002","url":null,"abstract":"Abstract The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields used in the time integration by splitting, for each particle, the time step into sub-steps such that each of these sub-steps corresponds to particle cell residence times. This reduces the spatial discretization error. Given the stochastic nature of the models, a key aspect is to derive estimations of the residence times that do not anticipate the future of the Wiener process. To that effect, the new algorithm relies on a virtual particle, attached to each stochastic one, whose mean conditional behavior provides free-of-statistical-bias predictions of residence times. After consistency checks, this new algorithm is validated on two representative test cases: particle dispersion in a statistically uniform flow and particle dynamics in a non-uniform flow.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"29 1","pages":"95 - 126"},"PeriodicalIF":0.9,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48076657","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}
引用次数: 2
Frontmatter 头版头条
Monte Carlo Methods and Applications Pub Date : 2023-03-01 DOI: 10.1515/mcma-2023-frontmatter1
{"title":"Frontmatter","authors":"","doi":"10.1515/mcma-2023-frontmatter1","DOIUrl":"https://doi.org/10.1515/mcma-2023-frontmatter1","url":null,"abstract":"","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"212 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136270828","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}
引用次数: 0
Linking the Monte Carlo radiative transfer algorithm to the radiative transfer equation 将蒙特卡罗辐射传递算法与辐射传递方程联系起来
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2023-01-27 DOI: 10.1515/mcma-2023-2001
P. J. Valades-Pelayo, M. Ramirez-Cabrera, A. Balbuena-Ortega
{"title":"Linking the Monte Carlo radiative transfer algorithm to the radiative transfer equation","authors":"P. J. Valades-Pelayo, M. Ramirez-Cabrera, A. Balbuena-Ortega","doi":"10.1515/mcma-2023-2001","DOIUrl":"https://doi.org/10.1515/mcma-2023-2001","url":null,"abstract":"Abstract This manuscript presents a short route to justify the widely used Monte Carlo Radiative Transfer (MCRT) algorithm straight from the Radiative Transfer Equation (RTE). In this regard, this paper starts deriving a probability measure obtained from the integral formulation of the RTE under a unidirectional point source in an infinite domain. This derivation only requires the analytical integration of the first two terms of a perturbation expansion. Although derivations have been devised to clarify the relationship between the MCRT and the RTE, they tend to be rather long and elaborate. Considering how simple it is to justify the MCRT from a loose probabilistic interpretation of the photon’s physical propagation process, the decay in popularity of former approaches relating MCRT to the RTE is entirely understandable. Unfortunately, all of this has given the false impression that MCRT and the RTE are not that closely related, to the point that recent works have explicitly stated that no direct link exists between them. This work presents a simpler route demonstrating how the MCRT algorithm emerges to statistically sample the RTE explicitly through Markov chains, further clarifying the method’s foundations. Although compact, the derivation proposed in this work does not skip any fundamental step, preserving mathematical rigor while giving specific expressions and functions. Thus, this derivation can help devise efficient ways to statistically sample the RTE for different scenarios or when coupling the MCRT method with other methods traditionally grounded in the RTE, such as the Spherical Harmonics and Discrete Ordinates methods.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"29 1","pages":"173 - 180"},"PeriodicalIF":0.9,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43267975","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}
引用次数: 0
Methodology for nonparametric bias reduction in kernel regression estimation 核回归估计中的非参数偏差约简方法
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2023-01-10 DOI: 10.1515/mcma-2022-2130
Y. Slaoui
{"title":"Methodology for nonparametric bias reduction in kernel regression estimation","authors":"Y. Slaoui","doi":"10.1515/mcma-2022-2130","DOIUrl":"https://doi.org/10.1515/mcma-2022-2130","url":null,"abstract":"Abstract In this paper, we propose and investigate two new kernel regression estimators based on a bias reduction transformation technique. We study the properties of these estimators and compare them with Nadaraya–Watson’s regression estimator and Slaoui’s (2016) regression estimator. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators, and the asymptotic MISE (mean integrated squared error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations and a real Malaria dataset.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"29 1","pages":"55 - 77"},"PeriodicalIF":0.9,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49604358","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}
引用次数: 0
Development and implementation of branching random walk on spheres algorithms for solving the 2D elastostatics Lamé equation 求解二维弹性静力学lam<s:1>方程的球上分支随机行走算法的开发与实现
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2023-01-10 DOI: 10.1515/mcma-2022-2131
I. Shalimova, K. Sabelfeld
{"title":"Development and implementation of branching random walk on spheres algorithms for solving the 2D elastostatics Lamé equation","authors":"I. Shalimova, K. Sabelfeld","doi":"10.1515/mcma-2022-2131","DOIUrl":"https://doi.org/10.1515/mcma-2022-2131","url":null,"abstract":"Abstract In this paper, we address a long-standing open problem in stochastic simulation: construction of a random walk on spheres (RWS) algorithm for solving a system of elasticity equations, known as the Lamé equation. Many attempts to generalize the classic probabilistic representations like the Kac formula for parabolic and scalar elliptic equations failed. A different approach based on a branching random walk on spheres (BRWS) introduced in our paper of 1995 [K. K. Sabelfeld and D. Talay, Integral formulation of the boundary value problems and the method of random walk on spheres, Monte Carlo Methods Appl. 1 1995, 1, 1–34] made little progress in solving this problem. In the present study, we further improve the BRWS algorithm by a special implementation of a branching anisotropic random walk on spheres process.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"29 1","pages":"79 - 93"},"PeriodicalIF":0.9,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46049317","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}
引用次数: 1
Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process 时间非均匀Ornstein-Uhlenbeck过程的参数最小二乘估计
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2022-11-02 DOI: 10.1515/mcma-2022-2127
G. Pramesti
{"title":"Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process","authors":"G. Pramesti","doi":"10.1515/mcma-2022-2127","DOIUrl":"https://doi.org/10.1515/mcma-2022-2127","url":null,"abstract":"Abstract We address the least-squares estimation of the drift coefficient parameter θ = ( λ , A , B , ω p ) theta=(lambda,A,B,omega_{p}) of a time-inhomogeneous Ornstein–Uhlenbeck process that is observed at high frequency, in which the discretized step size ℎ satisfies h → 0 hto 0 . In this paper, under the conditions n ⁢ h → ∞ nhtoinfty and n ⁢ h 2 → 0 nh^{2}to 0 , we prove the consistency and the asymptotic normality of the estimators. We obtain the convergence of the parameters at rate n ⁢ h sqrt{nh} , except for ω p omega_{p} at n 3 ⁢ h 3 sqrt{n^{3}h^{3}} . To verify our theoretical findings, we do a simulation study. We then illustrate the use of the proposed model in fitting the energy use of light fixtures in one Belgium household and the stock exchange.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"29 1","pages":"1 - 32"},"PeriodicalIF":0.9,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44053654","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}
引用次数: 1
Global random walk on grid algorithm for solving Navier–Stokes and Burgers equations 求解Navier-Stokes和Burgers方程的全局随机网格行走算法
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2022-10-28 DOI: 10.1515/mcma-2022-2126
K. Sabelfeld, Oleg Bukhasheev
{"title":"Global random walk on grid algorithm for solving Navier–Stokes and Burgers equations","authors":"K. Sabelfeld, Oleg Bukhasheev","doi":"10.1515/mcma-2022-2126","DOIUrl":"https://doi.org/10.1515/mcma-2022-2126","url":null,"abstract":"Abstract The global random walk on grid method (GRWG) is developed for solving two-dimensional nonlinear systems of equations, the Navier–Stokes and Burgers equations. This study extends the GRWG which we have earlier developed for solving the nonlinear drift-diffusion-Poisson equation of semiconductors (Physica A 556 (2020), Article ID 124800). The Burgers equation is solved by a direct iteration of a system of linear drift-diffusion equations, while the Navier–Stokes equation is solved in the stream function-vorticity formulation.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"293 - 305"},"PeriodicalIF":0.9,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43562871","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}
引用次数: 0
Simulation of drift-diffusion process at high Péclet numbers by the random walk on spheres method 用球上随机游走法模拟高psamclet数下的漂移扩散过程
IF 0.9
Monte Carlo Methods and Applications Pub Date : 2022-10-28 DOI: 10.1515/mcma-2022-2128
K. Sabelfeld, Ivan Aksyuk
{"title":"Simulation of drift-diffusion process at high Péclet numbers by the random walk on spheres method","authors":"K. Sabelfeld, Ivan Aksyuk","doi":"10.1515/mcma-2022-2128","DOIUrl":"https://doi.org/10.1515/mcma-2022-2128","url":null,"abstract":"Abstract In this paper, we address the problem of flow simulation at high Péclet numbers by the random walk on spheres (RWS) method. Conventional deterministic methods here face difficulties related to high solution gradients near the boundary in the region known as the boundary layer. In the finite-difference methods, this leads to introduction of very fine meshes which in turn causes problems of stability and high dimensions. The RWS algorithm is mesh free, but the high Péclet number flows should probably also affect the efficiency of simulations. However, it turns out that the RWS algorithm can be well adapted to this case. We present an analysis of the RWS algorithm for different examples of flows with high Péclet number. Simulations are carried out for different boundary conditions and for two-layered material with different diffusion coefficients of exciton’s mobility.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"349 - 367"},"PeriodicalIF":0.9,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42307771","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}
引用次数: 0
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