Pub Date : 2020-12-17DOI: 10.1007/978-3-030-98319-2_8
Max Hird, Samuel Livingstone, Giacomo Zanella
{"title":"A fresh Take on 'Barker Dynamics' for MCMC","authors":"Max Hird, Samuel Livingstone, Giacomo Zanella","doi":"10.1007/978-3-030-98319-2_8","DOIUrl":"https://doi.org/10.1007/978-3-030-98319-2_8","url":null,"abstract":"","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"38 1","pages":"169-184"},"PeriodicalIF":0.9,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81976348","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}
Pub Date : 2020-12-17DOI: 10.1007/978-3-030-98319-2_11
A. Cozma, C. Reisinger
{"title":"Simulation of conditional expectations under fast mean-reverting stochastic volatility models","authors":"A. Cozma, C. Reisinger","doi":"10.1007/978-3-030-98319-2_11","DOIUrl":"https://doi.org/10.1007/978-3-030-98319-2_11","url":null,"abstract":"","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"16 1","pages":"223-240"},"PeriodicalIF":0.9,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75703429","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}
Pub Date : 2020-12-15DOI: 10.1007/978-3-030-98319-2_12
M. Huber
{"title":"Generating from the Strauss Process using stitching","authors":"M. Huber","doi":"10.1007/978-3-030-98319-2_12","DOIUrl":"https://doi.org/10.1007/978-3-030-98319-2_12","url":null,"abstract":"","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"12 1","pages":"241-251"},"PeriodicalIF":0.9,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82058479","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}
Pub Date : 2020-12-15DOI: 10.1007/978-3-030-98319-2_14
M. Hofert, Avinash Prasad, Mu Zhu
{"title":"Applications of multivariate quasi-random sampling with neural networks","authors":"M. Hofert, Avinash Prasad, Mu Zhu","doi":"10.1007/978-3-030-98319-2_14","DOIUrl":"https://doi.org/10.1007/978-3-030-98319-2_14","url":null,"abstract":"","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"17 1","pages":"273-289"},"PeriodicalIF":0.9,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86001095","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}
Pub Date : 2020-12-15DOI: 10.1007/978-3-030-98319-2_9
P. Blondeel, Pieterjan Robbe, S. François, G. Lombaert, S. Vandewalle
{"title":"On the Selection of Random Field Evaluation Points in the p-MLQMC Method","authors":"P. Blondeel, Pieterjan Robbe, S. François, G. Lombaert, S. Vandewalle","doi":"10.1007/978-3-030-98319-2_9","DOIUrl":"https://doi.org/10.1007/978-3-030-98319-2_9","url":null,"abstract":"","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"1 1","pages":"185-203"},"PeriodicalIF":0.9,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86246927","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}
Pub Date : 2020-12-01DOI: 10.1515/mcma-2020-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/mcma-2020-frontmatter4","DOIUrl":"https://doi.org/10.1515/mcma-2020-frontmatter4","url":null,"abstract":"","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mcma-2020-frontmatter4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41816612","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 A Random Walk on Ellipsoids (RWE) algorithm is developed for solving a general class of elliptic equations involving second- and zero-order derivatives. Starting with elliptic equations with constant coefficients, we derive an integral equation which relates the solution in the center of an ellipsoid with the integral of the solution over an ellipsoid defined by the structure of the coefficients of the original differential equation. This integral relation is extended to parabolic equations where a first passage time distribution and survival probability are given in explicit forms. We suggest an efficient simulation method which implements the RWE algorithm by introducing a notion of a separation sphere. We prove that the logarithmic behavior of the mean number of steps for the RWS method remains true for the RWE algorithm. Finally we show how the developed RWE algorithm can be applied to solve elliptic and parabolic equations with variable coefficients. A series of supporting computer simulations are given.
{"title":"Random walk on ellipsoids method for solving elliptic and parabolic equations","authors":"I. Shalimova, K. Sabelfeld","doi":"10.1515/mcma-2020-2078","DOIUrl":"https://doi.org/10.1515/mcma-2020-2078","url":null,"abstract":"Abstract A Random Walk on Ellipsoids (RWE) algorithm is developed for solving a general class of elliptic equations involving second- and zero-order derivatives. Starting with elliptic equations with constant coefficients, we derive an integral equation which relates the solution in the center of an ellipsoid with the integral of the solution over an ellipsoid defined by the structure of the coefficients of the original differential equation. This integral relation is extended to parabolic equations where a first passage time distribution and survival probability are given in explicit forms. We suggest an efficient simulation method which implements the RWE algorithm by introducing a notion of a separation sphere. We prove that the logarithmic behavior of the mean number of steps for the RWS method remains true for the RWE algorithm. Finally we show how the developed RWE algorithm can be applied to solve elliptic and parabolic equations with variable coefficients. A series of supporting computer simulations are given.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"26 1","pages":"335 - 353"},"PeriodicalIF":0.9,"publicationDate":"2020-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mcma-2020-2078","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43214522","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}
E. Kablukova, K. Sabelfeld, D. Y. Protasov, K. Zhuravlev
Abstract Monte Carlo algorithms are developed to simulate the electron transport in semiconductors. In particular, the drift velocity in GaN semiconductors is calculated, and a comparison with experimental measurements is discussed. Explicit expressions for the scattering probabilities and distributions of the scattering angle of electrons on polar optical and intervalley phonons, and acoustic deformation potential as well are given. A good agreement of the simulation results and the experimental measurements reveals that the M-L valley is located at 0.7 eV higher than the Γ-valley. This value agrees with other experimental studies, while it is lower compared to ab initio calculations.
{"title":"Drift velocity in GaN semiconductors: Monte Carlo simulation and comparison with experimental measurements","authors":"E. Kablukova, K. Sabelfeld, D. Y. Protasov, K. Zhuravlev","doi":"10.1515/mcma-2020-2077","DOIUrl":"https://doi.org/10.1515/mcma-2020-2077","url":null,"abstract":"Abstract Monte Carlo algorithms are developed to simulate the electron transport in semiconductors. In particular, the drift velocity in GaN semiconductors is calculated, and a comparison with experimental measurements is discussed. Explicit expressions for the scattering probabilities and distributions of the scattering angle of electrons on polar optical and intervalley phonons, and acoustic deformation potential as well are given. A good agreement of the simulation results and the experimental measurements reveals that the M-L valley is located at 0.7 eV higher than the Γ-valley. This value agrees with other experimental studies, while it is lower compared to ab initio calculations.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"26 1","pages":"263 - 271"},"PeriodicalIF":0.9,"publicationDate":"2020-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mcma-2020-2077","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45427333","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 work, we propose a new method for calculating the mathematical expectation of nonlinear functionals from random processes. The method is based on using Wiener chaos expansion and approximate formulas, exact for functional polynomials of given degree. Examples illustrating approximation accuracy are considered.
{"title":"An approximate formula for calculating the expectations of functionals from random processes based on using the Wiener chaos expansion","authors":"A. Egorov","doi":"10.1515/mcma-2020-2074","DOIUrl":"https://doi.org/10.1515/mcma-2020-2074","url":null,"abstract":"Abstract In this work, we propose a new method for calculating the mathematical expectation of nonlinear functionals from random processes. The method is based on using Wiener chaos expansion and approximate formulas, exact for functional polynomials of given degree. Examples illustrating approximation accuracy are considered.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"26 1","pages":"285 - 292"},"PeriodicalIF":0.9,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mcma-2020-2074","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47835394","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 describe an implementation of the de-biased estimator using mixed sequences; these are sequences obtained from pseudorandom and low-discrepancy sequences. We use this implementation to numerically solve some stochastic differential equations from computational finance. The mixed sequences, when combined with Brownian bridge or principal component analysis constructions, offer convergence rates significantly better than the Monte Carlo implementation.
{"title":"Implementing de-biased estimators using mixed sequences","authors":"Arun Kumar Polala, G. Ökten","doi":"10.1515/mcma-2020-2075","DOIUrl":"https://doi.org/10.1515/mcma-2020-2075","url":null,"abstract":"Abstract We describe an implementation of the de-biased estimator using mixed sequences; these are sequences obtained from pseudorandom and low-discrepancy sequences. We use this implementation to numerically solve some stochastic differential equations from computational finance. The mixed sequences, when combined with Brownian bridge or principal component analysis constructions, offer convergence rates significantly better than the Monte Carlo implementation.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"26 1","pages":"293 - 301"},"PeriodicalIF":0.9,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/mcma-2020-2075","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45823111","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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