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摘要翻译：
我们提出了一个粒子滤波器的构造，用于一个表现出时间尺度分离的系统。时间尺度的分离允许我们利用两个简化：一）使用平均原理对每个粒子求解所需的系统进行降维；二）对转移概率进行因式分解，从而允许滤波步骤的Rao-Blackwellidation。这两个简化都可以使用粗投影积分框架来实现。所得粒子滤波器比基于原系统的粒子滤波器更快，方差更小。该方法在多尺度随机微分方程和化学反应驱动的多尺度纯跳跃扩散上进行了测试。
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英文标题：
《Variance reduction for particle filters of systems with time-scale
separation》
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作者：
Dror Givon, Panagiotis Stinis, and Jonathan Weare
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We present a particle filter construction for a system that exhibits time-scale separation. The separation of time-scales allows two simplifications that we exploit: i) The use of the averaging principle for the dimensional reduction of the system needed to solve for each particle and ii) the factorization of the transition probability which allows the Rao-Blackwellization of the filtering step. Both simplifications can be implemented using the coarse projective integration framework. The resulting particle filter is faster and has smaller variance than the particle filter based on the original system. The method is tested on a multiscale stochastic differential equation and on a multiscale pure jump diffusion motivated by chemical reactions.
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PDF链接：
https://arxiv.org/pdf/705.2262
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