共查询到19条相似文献,搜索用时 62 毫秒
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EM算法是近年来常用的求后验众数的估计的一种数据增广算法, 但由于求出其E步中积分的显示表达式有时很困难, 甚至不可能, 限制了其应用的广泛性. 而Monte Carlo EM算法很好地解决了这个问题, 将EM算法中E步的积分用Monte Carlo模拟来有效实现, 使其适用性大大增强. 但无论是EM算法, 还是Monte Carlo EM算法, 其收敛速度都是线性的, 被缺损信息的倒数所控制, 当缺损数据的比例很高时, 收敛速度就非常缓慢. 而Newton-Raphson算法在后验众数的附近具有二次收敛速率. 本文提出Monte Carlo EM加速算法, 将Monte Carlo EM算法与Newton-Raphson算法结合, 既使得EM算法中的E步用Monte Carlo模拟得以实现, 又证明了该算法在后验众数附近具有二次收敛速度. 从而使其保留了Monte Carlo EM算法的优点, 并改进了Monte Carlo EM算法的收敛速度. 本文通过数值例子, 将Monte Carlo EM加速算法的结果与EM算法、Monte Carlo EM算法的结果进行比较, 进一步说明了Monte Carlo EM加速算法的优良性. 相似文献
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系统生物学中的诸多现象,如生物化学反应过程、生态系统的演变、传染病的传播等,都可以用随机微分方程来描述.由于考虑了随机因素的影响,随机微分方程模型往往能比确定性的微分方程模型更为准确地刻画变量随时间的演化规律.但是随机微分方程的真解大多不可得到,有的即使可以求出真解,但解的形式极其复杂,用起来十分不便.因此,在计算机上对其进行数值仿真就显得十分必要.系统生物学中的随机微分方程模型一般呈现出高维、高度非线性、真解位于某些特定的区域等特点,对它们的数值模拟需要做专门的研究.本文概述求解几类常见的系统生物学模型(生物化学反应模型、生态系统模型、传染病模型、群体遗传学模型、细胞分化模型)的数值算法及这些数值算法各自的优缺点. 相似文献
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本文针对计及几何,材料,接触摩擦等耦合作用的高度非线性的加工成形过程数值模拟和计算分析工作,建议了非增量时-空求解算法。 相似文献
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应用Monte Carlo EM(MCEM)算法给出了多层线性模型参数估计的新方法,解决了EM算法用于模型时积分计算困难的问题,并通过数值模拟将方法的估计结果与EM算法的进行比较,验证了方法的有效性和可行性. 相似文献
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本文在Larson的“键长涨落模型”的基础上提出了模拟高浓度多链体系的新算法。本算法具有如下特征:(1)除通常的微松弛模式外,还直接引入了链的Reptation运动;(2)提出了空穴扩散算法使体系随时间演化。由于本算法的这些新特征,克服了前人的算法不能运用于两维体系以及高浓度多链体系的缺点,同时也大大缩短了计算耗时。应用本文的算法,在44×44的元胞中模拟了链长为21,浓度为0.9545的体系的动力学行为。所得结果与Rouse理论的预言相符合。 相似文献
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《数学的实践与认识》2015,(21)
在随机波动模型下,研究亚式期权的定价问题.推导出了标的资产及其随机波动模型的路径,利用对偶变量法对亚式期权进行数值模拟计算,并对随机波动模型下与B-S模型下的欧式期权和亚式期权定价结果进行比较,最后给出了具有固定敲定价格和浮动敲定价格的算术亚式期权的数值计算结果. 相似文献
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复合材料弹性结构的高精度多尺度算法与数值模拟 总被引:5,自引:0,他引:5
1.引言 由于复合材料结构物理参数的非均匀各向异性以及细部几何构形的复杂性,在计算它的位移场、应力、应变场时,传统的有限元法因网格生成困难和计算规模太大而难以实现.70年代初,I.Babuska,J.L.Lions等人针对复合材料弹性结构提出了均匀化方法,见文[1],数值实验表明,均匀化方法对描述复合材料弹性结构的有效材料常数及刚度性质是有效的,但它不能刻画应力和应变场的局部变化,因而作为复合材料强度理论的判断依据,均匀化理论显然是不够的.为此,J.L.Lions,O.A.Oleinik等分别就… 相似文献
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考虑到金融时间序列的厚尾性即呈现尖峰厚尾分布,波动率具有聚集性和持续性等特点,也即标的资产的价格可能会出现间断的跳跃,我们展示了在标的资产价格对数收益服从NIG-Levy过程的条件下,如何构建和计算等价鞅测度,我们考虑通过Esscher转换得到Q等价鞅测度,并以此为基础寻找风险中性概率的条件,最后利用这些条件探讨亚式期权的数值定价问题,利用低差异序列中的Halton、Sobol、Faure序列对亚式期权进行了数值定价分析. 相似文献
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We have recently developed a global optimization methodology for solving combinatorial problems with either deterministic or stochastic performance functions. This method, the Nested Partitions (NP) method has been shown to generate a Markov chain and with probability one to converge to a global optimum. In this paper, we study the rate of convergence of the method through the use of Markov Chain Monte Carlo (MCMC) methods, and use this to derive stopping rules that can be applied during simulation-based optimization. A numerical example serves to illustrate the feasibility of our approach. 相似文献
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Implementable Algorithm for Stochastic Optimization Using Sample Average Approximations 总被引:1,自引:0,他引:1
We develop an implementable algorithm for stochastic optimization problems involving probability functions. Such problems arise in the design of structural and mechanical systems. The algorithm consists of a nonlinear optimization algorithm applied to sample average approximations and a precision-adjustment rule. The sample average approximations are constructed using Monte Carlo simulations or importance sampling techniques. We prove that the algorithm converges to a solution with probability one and illustrate its use by an example involving a reliability-based optimal design. 相似文献
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研究非仿射随机波动率模型的欧式障碍期权定价问题时,首先介绍了非仿射随机波动率模型,其次利用投资组合和It^o引理,得到了该模型下扩展的Black-Schole偏微分方程.由于这个方程没有显示解,因此采用对偶蒙特卡罗模拟法计算欧式障碍期权的价格.最后,通过数值实例验证了算法的可行性和准确性. 相似文献
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Summary Simulation can be defined as a numerical technique for conducting experiments on a digital computer, which involves certain
types of mathematical and logical models that describe the behaviour of a system over extended periods of real time. Simulation
is, in a wide sense, a technique for performing sampling experiments on a model of the system. Stochastic simulation implies
experimenting with the model over time including sampling stochastic variates from probability distributions. This paper describes
the main concepts of the application of Stochastic Simulation and Monte Carlo methods to the analysis of the operation of
electric energy systems, in particular to hydro-thermal generating systems. These techniques can take into account virtually
all contingencies inherent in the operation of the system. Also, the operating policies that have an important effect on the
performance of these systems can be realistically represented. 相似文献
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A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of pricing Asian options under the Heston stochastic volatility model. 2000 Mathematics Subject Classification, 65C30, 65C05. 相似文献
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Christophe Barrera-Esteve Florent Bergeret Charles Dossal Emmanuel Gobet Asma Meziou Rémi Munos Damien Reboul-Salze 《Methodology and Computing in Applied Probability》2006,8(4):517-540
In the natural gas market, many derivative contracts have a large degree of flexibility. These are known as Swing or Take-Or-Pay options. They allow their owner to purchase gas daily, at a fixed price and according to a volume of their choice. Daily,
monthly and/or annual constraints on the purchased volume are usually incorporated. Thus, the valuation of such contracts
is related to a stochastic control problem, which we solve in this paper using new numerical methods. Firstly, we extend the
Longstaff–Schwarz methodology (originally used for Bermuda options) to our case. Secondly, we propose two efficient parameterizations
of the gas consumption, one is based on neural networks and the other on finite elements. It allows us to derive a local optimal
consumption law using a stochastic gradient ascent. Numerical experiments illustrate the efficiency of these approaches. Furthermore,
we show that the optimal purchase is of bang-bang type.
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