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1.
近年来,一类由Itô随机微分方程驱动的奇异随机系统因其在实际领域中的广泛应用而备受关注.然而,系统方程同时包含奇异矩阵和扩散矩阵,大大增加了分析问题的复杂性.本文首先概述了奇异Itô随机系统几个重要基础问题的研究进展,主要包括:系统方程解的存在条件、广义Itô公式、容许性定义及稳定性问题.同时针对不同文献对上述问题的研究结果提出了自己的观点.最后对以上基础问题研究待解决的问题进行了展望. 相似文献
2.
本文回顾了近年来随机微分方程数值方法的稳定性的研究成果.作为相关话题,收敛性问题也有所涉猎.以经典Itô型随机微分方程、中立型随机泛函微分方程、Markov跳随机微分方程和Poisson跳随机微分方程为代表,主要介绍了几类数值方法稳定性研究的成果.这些方法包括常见的Euler-Maruyama方法、Backward Euler-Maruyama方法、θ方法、分步方法等.文中分析了关于稳定性等价性定理经典论文的学术思路,提出了随机微分方程数值计算与仿真所面临的挑战及所要解决的问题. 相似文献
3.
研究了一类Itô型随机时滞分布参数系统的滑动模控制问题,设计了该系统的变结构控制器,证明了系统的滑动模运动的存在性,并分析了在滑动切换面上滑动模控制系统关于不确定量的不变性特征及运动稳定性.与相关论文相比,所获结论与扩散系数相关,在实际应用中更具实践意义.运用文中方法,类似论文结论均可进行改进. 相似文献
4.
针对延迟中立型神经网络系统,研究了反馈控制问题.考虑了带有Le''vy噪声的中立型神经网络,建立了一个适当的Lyapunov函数.通过Lyapunov分析方法并使用一般性Itô公式和LMI技术,得到了闭环系统的均方稳定性准则.最后,通过数值例子证实本文方法的有效性. 相似文献
5.
主要研究金融领域中的多种数学模型,重点是利用R软件进行数值模拟.继续讨论更多的随机微分方程(SDE)模型,包括均值回归过程、均值回归的Ornstein-Uhlenbeck(OU)过程、平方根过程、CIR模型以及Θ过程.进一步,将对当前SDE数值解的研究给出更深入的建议. 相似文献
6.
主要研究了分数阶混合随机泛函微分方程的能控性.在无限维空间下,假设所考虑方程线性部分生成半群不是紧的,使用非紧性测度技术和Mönch不动点定理,给出了方程能控性充分条件,并通过一个例子说明了结论的有效性. 相似文献
7.
研究了随机滞后微分方程的一致有界和一致最终有界.利用Lyapunov函数和Razumikhin技巧,得到了一些关于随机滞后微分方程有界性新的Razumikhin定理,同时,证明随机滞后微分方程解的存在性,推广了相关的文献.最后,给出例子证实定理的有效性. 相似文献
8.
随机强迫对集合预报效果的影响研究 总被引：2，自引：0，他引：2
以Lorenz96模式为动力框架,建立了考虑模式随机强迫不确定性的集合预报系统,并选择模式气候态和集合平均预报效果为研究对象,研究随机强迫对集合预报效果的影响.结果表明,在数值模式积分过程中引入恰当的随机强迫构成的新计算范式,较非随机强迫更接近真值的气候平均与气候标准差,对刻画数值模式的气候态也有正效果;且随机强迫的正效果主要体现在长时效阶段.集合平均预报方面,绝大部分白噪声随机强迫对应的集合预报效果优于非随机强迫集合预报,集合预报效果也随白噪声强迫增大非单调变化,并且非线性系统不同,相同比率的白噪声随机强迫产生的效果也不同.同时,绝大部分红噪声随机强迫对应的集合预报效果也优于非随机强迫集合预报,但仅部分φ(表示所引入外强迫的随机性部分和确定性部分相互耦合的一个度量)值对应的红噪声强迫集合预报优于白噪声随机强迫集合预报;而且红噪声随机强迫集合预报改善效果随系数的正负分布非对称且非单调变化.此外,相关系数φ的选择也依赖于模型. 相似文献
9.
毛学荣 《南京气象学院学报》2017,9(3):246-261
本文对混杂随机时滞微分方程的当前发展及最新的研究成果进行了概述.主要回顾了混杂随机微分方程解的存在唯一性定理、稳定性、鲁棒有界性以及离散时间反馈镇定性等部分对混杂随机微分方程的研究起到关键推动作用的成果. 相似文献
10.
运用Lyapunov函数方法,基于泛函微分方程的不变原理、随机分析理论以及自适应反馈控制技术,给出了具有Markov切换的随机神经网络混合时滞依赖的自适应同步的充分性判据,它与线性矩阵不等式方法相比更容易验证.最后,通过一个数值模拟例子验证了理论结果的正确性及有效性. 相似文献
11.
主要研究了Black-Scholes模型.与Black-Scholes期权定价公式相比,将再次强调和证实利用R软件Monte Carlo模拟的强大作用. 相似文献
12.
主要研究了随机对数线性(SLL)模型以及如何基于SLL模型计算欧式期权平均收益.此外,还演绎了资产价格的Monte Carlo模拟. 相似文献
13.
主要讨论了 Cox-Ross-Rubinstein (CRR) 模型和广义的CRR模型,并研究了如何基于CRR模型和广义的CRR模型利用Monte Carlo模拟计算资产价格以及期权价值. 相似文献
14.
The general Ekman momentum approximation boundary-layer model(GEM) can be effectively used to describe the physical processes of the boundary layer. However, eddy viscosity, which is an approximated value, can lead to uncertainty in the solutions. In this paper, stochastic eddy viscosity is taken into consideration in the GEM, and generalized polynomial chaos is used to quantify the uncertainty. The goal of uncertainty quantification is to investigate the effects of uncertainty in the eddy viscosity on the model and to subsequently provide reliable distribution of simulation results. The performances of the stochastic eddy viscosity and generalized polynomial chaos method are validated based on three different types of eddy viscosities, and the results are compared based on the Monte Carlo method. The results indicate that the generalized polynomial chaos method can be accurately and efficiently used in uncertainty quantification for the GEM with stochastic eddy viscosity. 相似文献
15.
Despite recent advances in supercomputing, current general circulation models poorly represent the variability associated with organized tropical convection. In a recent study, the authors have shown, in the context of a paradigm two baroclinic mode system, that a stochastic multicloud convective parameterization based on three cloud types (congestus, deep and stratiform) can be used to improve the variability and the dynamical structure of tropical convection. Here, the stochastic multicloud model is modified with a lag type stratiform closure and augmented with an explicit mechanism for congestus detrainment moistening. These modifications improve the representation of intermittent coherent structures such as synoptic and mesoscale convective systems. Moreover, the new stratiform-lag closure allows for increased robustness of the coherent features of the model with respect to the amount of stochastic noise and leading to a multi-scale organization of slowly moving waves envelopes in which short-lived and chaotic convective events persist. Congestus cloud decks dominate the suppressed-dry phase of the wave envelopes. The simulations with the new closure have a higher amount of stochastic noise and result in a Walker type circulation with realistic mean and coherent variability which surpasses results of previous deterministic and stochastic multicloud models in the same parameter regime. Further, deterministic mean field limit equations (DMFLE) for the stochastic multicloud model are considered. Aside from providing a link to the deterministic multicloud parameterization, the DMFLE allow a judicious way of determining the amount of deterministic and stochastic “chaos” in the system. It is shown that with the old stratiform heating closure, the stochastic process accounts for most of the chaotic behavior. The simulations with the new stratiform heating closure exhibit a mixture of stochastic and deterministic chaos. The highly chaotic dynamics in the simulations with congestus detrainment mechanism is due to the strongly nonlinear and numerically stiff deterministic dynamics. In the latter two cases, the DMFLE can be viewed as a “standalone” parameterization, which is capable of capturing some dynamical features of the stochastic parameterization. Furthermore, it is shown that, in spatially extended simulations, the stochastic multicloud model can capture qualitatively two local statistical features of the observations: long and short auto-correlation times of moisture and precipitation, respectively and the approximate power-law in the probability density of precipitation event size for large precipitation events. The latter feature is not reproduced in the column simulations. This fact underscores the importance of gravity waves and large scale moisture convergence. 相似文献
16.
The El Niño stochastic oscillator 总被引：1，自引：1，他引：0
G. Burgers 《Climate Dynamics》1999,15(7):521-531
A stochastic model is fitted to the observed NINO3.4 time series between 1951–1995. The model is nothing more than the complex version of a first-order autoregressive process. The autocorrelation of this stochastic oscillator model is an exponentially decaying cosine, specified by three parameters: a period, a decay time, and a phase shift. It fits the observed NINO3.4 autocorrelation quite well. Anomalies during an El Niño can be characterized to a large extent by a single, irregularly oscillating, index. Equatorial wave dynamics and delayed-oscillator models have been used to explain this behaviour, and it has been suggested that El Niño might be a stable phenomenon excited by weather noise. Assuming this is the case, the stochastic oscillator has a direct physical interpretation: the parameters of the oscillation can be linked to dynamical models of the delayed-oscillator type, and the noise terms represent random influences, such as intraseasonal oscillations. Long Monte Carlo simulations with the stochastic oscillator show substantial decadal variability and variation in predictability. The observed decadal variability is comparable, except for the rather large rise in the long-term mean around 1980. The observed seasonal dependence of El Niño behaviour is not compatible with the natural variability of a stationary stochastic oscillator. Formulating the model in terms of standardized anomalies takes into account some of the seasonal dependence. A stochastic oscillator forecast model has a skill approaching that of more comprehensive statistical models and may thus serve as an appropriate baseline for the skill of El Niño forecasting systems. 相似文献
17.
随机天气模型参数化方案的研究及其模拟能力评估 总被引：8，自引：2，他引：6
文中介绍了随机天气模型 WGEN的基本结构及其模拟原理 ,并针对其中随机过程的统计结构特征和 GCMs输出要素的不同时空尺度特点 ,利用动态数据的参数化分析方法等统计学技术 ,确定了该模型参数的估计方法。同时基于蒙特卡罗数值计算原理 ,给出了 WGEN的随机试验方法 ,并通过模拟基准气候 ,从时间分布和空间场两方面对模型在中国东北地区的模拟效果及其能力进行了评估。结果表明 ,模型对于最高气温、最低气温、降水和辐射等要素均具有较好的模拟效果 ,模拟序列与观测序列的取值分布有较一致的概率特性。由此可以结合 GCMs大尺度网格上输出的月和年要素值 ,通过调控随机过程的参数 ,生成具有不同气候变率的 2× CO2 逐日气候变化情景 ,实现气候预测模式与气候影响模式的嵌套 ,进一步研究气候变率变化的可能影响。 相似文献
18.
预报检验重点关注预报与观测间的综合统计特征用以探讨模式预报性能,而统计显著性检验方法是衡量评估结论的重要指标,是判断预报效果改进与否的有效手段.当前诸多重要检验指标如降水技巧评分等由于不满足正态分布特征均难以采用简单的计算方式获得置信区间以衡量检验指标的误差特征,因此难以正确判断通过统计检验所获得的评估差异是真实反映模式预报效果差异或是由检验样本的不确定性所造成.蒙特卡罗方法可通过样本重构获取正态分布的统计样本从而有效地解决这一问题.采用2015年8月的T639模式及GRAPES全球预报模式24 h降水预报产品,使用中国区域2400站日降水资料作为实况,重点研究蒙特卡罗方法在统计显著性检验中的应用特征,分析不同蒙特卡罗重构次数对检验结果的收敛性.结果表明10 000次蒙特卡罗重构后统计指标可满足正态分布,而通过显著性检验分析后可明显区分预报系统间降水评分差异的统计特征. 相似文献
19.
Richard b. Howarth 《Climatic change》2003,56(3):257-263
Monte Carlo simulations by Tol (2003) suggest that there is a small but positive probability that climate change will impose catastrophic impacts on future society unless sufficient steps are taken to reduce greenhouse gas emissions. This paper critically evaluates this finding and its implications for policy analysis and decision-making. 相似文献
