The estimation of probability distribution of SDE by only one sample trajectory

This paper focuses on the method of the simulation of a stochastic system and the main method of our paper is the Monte Carlo computation simulation method. Taking the stochastic Logistic equation as an example, we present the simulation of the sample trajectory by Euler scheme and the invariant probability distribution of stochastic differential equations with the Monte Carlo method. We also compare the simulation result with the analytical result for the autonomous stochastic Logistic model. Moreover, the stochastic Logistic equation with Markovian switching which is described by a Markov chain taking values in a finite state space is considered.     

二元自由基共聚合的Monte Carlo模拟

采用Monte Carlo模拟计算方法、可视化编程语言Visual Basic,以研究非稳态、考虑前末端效应、聚合反应可逆等情况下二元自由基共聚合反应,以期得到共聚物的瞬时组成、组成分布、序列分布等决定共聚物效能的重要参数。以数值模拟代替实际实验,不仅可节约成本,而且可减少工作量。模拟结果显示,Monte Carlo模拟值与实验值符合较好,说明本模拟过程模拟效果较好,结果可靠,可用来模拟未知共聚合体系,并为实际共聚物的合成提供帮助。     

毁伤概率评估的加权蒙特卡洛方法

由于经典蒙特卡洛方法的仿真效率不高,文中利用概率论和数理统计的基本原理,可以推导得到加权蒙特卡洛方法.加权蒙特卡罗方法不但能有效的缩小了样本方差,还能提高目标事件出现概率,相当于提高了样本的抽样效率,从而提高了仿真效率.与此同时,文中分别利用经典蒙特卡洛和加权蒙特卡洛这两种方法对典型目标进行了仿真计算,仿真计算最终证明了加权蒙特卡洛方法的仿真效率明显优于经典蒙特卡洛方法,能使仿真工作量成数量级的衰减.     

反跑道集束战斗部毁伤概率研究

该文采用蒙特卡洛方法，建立反跑道集束战斗部毁伤概率的数学模型，给出了计算毁伤概率的仿真算法，开发相应仿真软件，并给出具体的仿真算例和仿真分析，最后，对影响毁伤概率的诸因素进行了讨论。     

Reliability estimation for dynamical systems subject to stochastic excitation using subset simulation with splitting

A new subset simulation approach is proposed for reliability estimation for dynamical systems subject to stochastic excitation. The basic idea of subset simulation is to factor a small failure probability into a product of larger failure probabilities conditional on intermediate failure events. The new method proposed in this work does not require Markov Chain Monte Carlo simulation, in contrast to the original method, to estimate the conditional probabilities; instead, only direct Monte Carlo simulation is needed. The method employs splitting of a trajectory that reaches an intermediate failure level into multiple trajectories subsequent to the corresponding first passage time. The new approach still enjoys most of the advantages of the original subset simulation, e.g. it is applicable to general causal dynamical systems and it is robust with respect to the dimension of the uncertain input variables. The statistical properties of the failure probability estimators are presented, where it is shown that they are unbiased and formulas are derived to assess the error of estimation, including the coefficient of variation. We also discuss the selection of intermediate failure events and the number of samples for each failure level. The resulting algorithm is simple and easy to implement. Two examples are presented to demonstrate the effectiveness of the new approach, and the results are compared with the original subset simulation and with direct Monte Carlo simulation.     

基于蒙特卡罗的星-地单光子通信仿真方法

针对星-地单光子通信研究现状和复杂系统特性,提出一种运用蒙特卡罗方法研究星-地单光子通信全链路仿真过程的方法。基于离散事件仿真器构建星-地单光子通信的全链路仿真系统,采用蒙特卡罗方法对单光子通信过程进行大量模拟计算,得到准确的统计分析结果。仿真考虑了多种影响因素,对系统的关键性能参数做出综合、准确的评价,为系统的设计和优化提供依据,验证蒙特卡罗仿真在单光子通信系统中的可用性。     

体系对抗仿真中实验次数的自适应控制方法

在方案优化过程中,为消除随机因素的影响,需要进行蒙特卡洛仿真。为此,提出将置信区间引入到体系对抗仿真中,根据仿真过程中产生的数据样本确定蒙特卡洛仿真是否结束。依据数据样本的特性,对置信区间法进行相应的扩展,在获取满足精度需求的解的条件下,尽量缩减仿真实验次数。仿真实验结果表明,扩展置信区间法能够具备对蒙特卡洛仿真的自适应控制能力。     

Grand canonical auxiliary field Monte Carlo: a new technique for simulating open systems at high density

The computation of open many-particle systems at high densities is a major challenge since many decades due to the inherent limitations of grand canonical simulation methods based on particle exchange algorithms. In this paper we report on the statistical convergence behavior in the high density regime of a recently developed alternative called the grand canonical auxiliary field Monte Carlo method. We show on a common soft matter model widely used in polymer simulation that it possesses a more appropriate statistical behavior in the dense regime than the currently employed grand canonical Monte Carlo methods relying on particle exchange algorithms.     

Monte Carlo方法与计算机模拟应用研究

介绍了Monte Carlo方法,提出其在模拟Buffer问题时存在的一个问题,并给出改进的方法;提出了用Monte Carlo方法产生任意分布随机变量的原理及方法,并对Beta分布和标准正态分布随机变量进行了计算机模拟和效果检验。     

LDPC码的错误平层研究*

摘要：为了更好的研究LDPC码的错误平层现象,本文提出了一种利用重要抽样信息的仿真方法。在AWGN信道下,当误比特率极低时,该方法相比于传统的蒙特卡洛方法在保证仿真质量不变的情况下,取得了极高的仿真增益。利用该方法可以仿真到传统蒙特卡罗方法无法仿真到的仿真区域。仿真结果表明,对于一个码长为2000,码率为1/2的LDPC码字,当误比特率为10-20 时,该方法取得1014以上的仿真增益。     

蒙特卡罗仿真机及其应用

蒙特卡罗仿真机是通过对随机性问题采用Monte Carlo方法进行计算机仿真，从而得出待解问题的解。为了研究复杂的随机问题，文中提出了基于蒙特卡罗的随机模拟法的蒙特卡罗仿真机，并说明了它的基本原理。通过圆周率的计算，实践了蒙特卡罗仿真机的应用过程，从而显示出蒙特卡罗仿真法处理随机性问题的优越性和仿真普遍的适用性。     

Manifold Next Event Estimation

We present manifold next event estimation (MNEE), a specialised technique for Monte Carlo light transport simulation to render refractive caustics by connecting surfaces to light sources (next event estimation) across transmissive interfaces. We employ correlated sampling by means of a perturbation strategy to explore all half vectors in the case of rough transmission while remaining outside of the context of Markov chain Monte Carlo, improving temporal stability. MNEE builds on differential geometry and manifold walks. It is very lightweight in its memory requirements, as it does not use light caching methods such as photon maps or importance sampling records. The method integrates seamlessly with existing Monte Carlo estimators via multiple importance sampling.     

贷款组合信用风险模拟的简化方法

金融机构对贷款组合风险管理的通常方法是在VaR框架下,用蒙特卡罗模拟模拟技术估计期末贷款组合价值分布来计算最大损失.但模拟技术会产生极大的计算工作量.提出了运用计算机模拟技术对贷款组合信用风险(Value at Risk,VaR)的蒙特卡罗模拟进行简化的方法,把一个贷款组合在每个信用评级级别划分为子贷款组合,用同类子贷款组合的非预期损失来获得不同类子贷款组合的最大损失.以期节省运行时间,提高计算效率.模拟结果表明利用该方法计算贷款组合信用风险VaR效率高,能够较准确地获得信用风险值.     

基于蒙特卡罗模拟修正的随机矩阵去噪方法

针对蕴含噪声信息较少的小组合股票市场,提出使用蒙特卡罗模拟修正的随机矩阵去噪方法。首先通过数据模拟生成随机矩阵,然后利用大量的模拟数据来同时修正噪声下界和上界,最终对噪声范围进行精确测定。运用道琼斯中国88指数和香港恒生50指数的数据进行实证分析,结果表明,与LCPB法、PG+法和KR法相比,在特征值、特征向量和反比参率方面, 蒙特卡罗模拟去噪方法修正后噪声范围的合理性及有效性得到很大的提升;对去噪前后的相关矩阵进行投资组合,得知在相同的期望收益率下,蒙特卡罗模拟去噪方法具有最小的风险值,能够为资产组合选择和风险管理等金融应用提供一定的参考。     

Integrating subset simulation with probabilistic re-analysis to estimate reliability of dynamic systems

It is often expensive to estimate the failure probability of highly reliable systems by Monte Carlo simulation. Subset Simulation breaks the original problem of estimating a small probability into the estimation of a sequence of large conditional probabilities, which is more efficient. The conditional probabilities are estimated by Markov Chain simulation. Uncertainty in the power spectral density of the excitation makes it necessary to re-evaluate the reliability for many power spectral densities that are consistent with the evidence about the system excitation. Subset Simulation is more efficient than Monte Carlo simulation, but still requires a new simulation for each admissible power spectral density. This paper presents an efficient method to re-evaluate the reliability of a dynamic system under stationary Gaussian stochastic excitation for different load spectra. We accomplish that by re-weighting the results of a single Subset Simulation. This method is applicable to both linear and nonlinear systems provided that all of the spectra contain the same amount of energy. The authors are currently working on an extension of the method to nonlinear systems, even when the sampling and true power spectral density functions contain different amounts of energy.     

薄层中药物释放的Monte Carlo模拟

描述了一种用于研究药物由搽剂经角质层转运至受体过程的直接Monte Carlo模拟方法。对角质层药物浓度为零和搽剂与角质层药物浓度处于平衡两种初始条件下的药物转运过程进行了模拟。与解析Laplace变换结合数值求逆的结果比较表明,这种Monte Carlo模拟方法准确、可靠、方便,很容易用于更复杂的体系。     

蒙特卡罗法在调制解调中的应用

在加性高斯噪声干扰条件下的2FSK和16QAM调制解调方法基础上,根据蒙特卡罗仿真方法基本思想,建立在加性噪声干扰下的相关检测系统蒙特卡罗仿真模型。模型通过Matlab软件方法实现,最终仿真结果与对应系统的理论误码率基本符合。     

A new simulation approach to the freezing transition

The task of accurately locating fluid-crystal phase boundaries by computer simulation is hampered by problems associated with traversing mixed-phase states. We describe a recently introduced Monte Carlo (MC) method that circumvents this problem by implementing a global coordinate transformation (“phase switch”) which takes the system from one pure phase to the other in a single MC step. The method is potentially quite general. We illustrate it by application to the freezing of hard spheres.     

Computing the principal eigenvalue of the Laplace operator by a stochastic method

We describe a Monte Carlo method for the numerical computation of the principal eigenvalue of the Laplace operator in a bounded domain with Dirichlet conditions. It is based on the estimation of the speed of absorption of the Brownian motion by the boundary of the domain. Various tools of statistical estimation and different simulation schemes are developed to optimize the method. Numerical examples are studied to check the accuracy and the robustness of our approach.