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Stochastic Simulation and Monte Carlo Methods: Mathematical Foundations of Stochastic Simulation
Denis Talay,Carl Graham +1 more
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TLDR
In this article, the authors present the principles of Monte Carlo Methods, Girsanov's Theorem, and Stochastic Algorithms for Markov Processes with Jumps.Abstract:
Part I:Principles of Monte Carlo Methods.- 1.Introduction.- 2.Strong Law of Large Numbers and Monte Carlo Methods.- 3.Non Asymptotic Error Estimates for Monte Carlo Methods.- Part II:Exact and Approximate Simulation of Markov Processes.- 4.Poisson Processes.- 5.Discrete-Space Markov Processes.- 6.Continuous-Space Markov Processes with Jumps.- 7.Discretization of Stochastic Differential Equations.- Part III:Variance Reduction, Girsanov's Theorem, and Stochastic Algorithms.- 8.Variance Reduction and Stochastic Differential Equations.- 9.Stochastic Algorithms.- References.- Index.read more
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Journal ArticleDOI
Estimation of national, regional, and global prevalence of alcohol use during pregnancy and fetal alcohol syndrome: a systematic review and meta-analysis
Svetlana Popova,Shannon Lange,Shannon Lange,Charlotte Probst,Charlotte Probst,Gerrit Gmel,Gerrit Gmel,Jürgen Rehm +7 more
TL;DR: The global prevalence of alcohol use during pregnancy was estimated to be 9·8% and the estimated prevalence of FAS in the general population was 14·6 per 10 000 people (95% CI 9·4-23·3).
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Global Prevalence of Fetal Alcohol Spectrum Disorder Among Children and Youth: A Systematic Review and Meta-analysis
Shannon Lange,Shannon Lange,Charlotte Probst,Charlotte Probst,Gerrit Gmel,Gerrit Gmel,Jürgen Rehm,Larry Burd,Svetlana Popova +8 more
TL;DR: The global prevalence of FASD among children and youth in the general population was estimated to be 7.7 per 1000 population (95% CI, 4.9-11.6 per 1000), and the global mean prevalence weighted by the number of live births in each country was estimated as mentioned in this paper.
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National, regional, and global prevalence of smoking during pregnancy in the general population: a systematic review and meta-analysis.
TL;DR: These findings should inform smoking prevention programmes and health promotion strategies as well as access to smoking cessation programmes.
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Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations
TL;DR: The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined deep learning, revolutionized the area of deep learning.
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On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations
TL;DR: In this article, the authors proposed a family of approximation methods based on Picard approximations and multilevel Monte Carlo methods and showed under suitable regularity assumptions on the exact solution of a semilinear heat equation that the computational complexity is bounded by