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Strong approximation of a two-factor stochastic volatility model under local Lipschitz condition 局部Lipschitz条件下双因素随机波动模型的强逼近
Q4 Mathematics Pub Date : 2023-11-11 DOI: 10.1515/mcma-2023-2021
Emmanuel Coffie
Abstract We establish theoretical properties of the solution to a two-variance-driven interest rate model with super-linear coefficient terms. Since this model is not tractable analytically, we construct an implementable numerical method to approximate it and prove the finite-time strong convergence theory under the local Lipschitz condition. Finally, we provide simulation examples to demonstrate the theoretical results.
摘要建立了具有超线性系数项的双方差驱动利率模型解的理论性质。由于该模型不可解析处理,我们构造了一种可实现的数值逼近方法,并证明了局部Lipschitz条件下的有限时间强收敛理论。最后,通过仿真实例对理论结果进行了验证。
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引用次数: 0
Stochastic simulation of electron transport in a strong electrical field in low-dimensional heterostructures 低维异质结构中强电场中电子输运的随机模拟
Q4 Mathematics Pub Date : 2023-11-01 DOI: 10.1515/mcma-2023-2019
Evgeniya Kablukova, Karl K. Sabelfeld, Dmitry Protasov, Konstantin Zhuravlev
Abstract In this paper we develop a stochastic simulation algorithm for electron transport in a DA-pHEMT heterostructure. Mathematical formulation of the problem of electron gas transport in the heterostructure in the form of a coupled system of Poisson, Schrödinger and kinetic Boltzmann equations is given. A Monte Carlo model of electron transport in DA-pHEMT heterostructures which accounts for multivalley parabolic band structure, as well as relevant formulas for calculating electron scattering rates and scattering phase functions on polar optical, intervalley phonons and on impurities are developed. The results of a computational experiment involving the solution of the system of Poisson–Schrödinger–Boltzmann equations for the AlGaAs / GaAs / InGaAs / GaAs / AlGaAs heterostructure are presented. The distribution of electrons by energy subband in the main and satellite valleys and the field dependences of the electron drift velocity in each valley are calculated. It was discovered that there is no spatial transfer of electrons into wide-gap AlGaAs layers due to high barriers created by modulated-doped impurities. A comparative analysis of the electron drift velocities in the studied DA-pHEMT heterostructures and in the unstrained layer of the InGaAs is given.
摘要本文提出了一种随机模拟DA-pHEMT异质结构中电子输运的算法。给出了异质结构中电子气体输运问题的泊松方程、Schrödinger方程和动力学玻尔兹曼方程耦合系统的数学表达式。建立了考虑多谷抛物带结构的DA-pHEMT异质结构中电子输运的蒙特卡罗模型,以及电子在极性光学、谷间声子和杂质上的散射速率和散射相函数的计算公式。本文给出了求解AlGaAs / GaAs / InGaAs / GaAs / AlGaAs异质结构Poisson-Schrödinger-Boltzmann方程组的计算实验结果。计算了电子在主谷和卫星谷的能量子带分布以及电子在各谷漂移速度的场依赖关系。研究发现,由于调制掺杂杂质产生的高势垒,没有电子在宽间隙AlGaAs层中的空间转移。比较分析了电子在DA-pHEMT异质结构和InGaAs非应变层中的漂移速度。
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引用次数: 0
Existence and uniqueness of solutions for perturbed stochastic differential equations with reflected boundary 具有反射边界的摄动随机微分方程解的存在唯一性
Q4 Mathematics Pub Date : 2023-10-24 DOI: 10.1515/mcma-2023-2018
Faiz Bahaj, Kamal Hiderah
Abstract In this paper, under some suitable conditions, we prove existence of a strong solution and uniqueness for the perturbed stochastic differential equations with reflected boundary (PSDERB), that is, { x ( t ) = x ( 0 ) + 0 t σ ( s , x ( s ) ) d B ( s ) + 0 t b ( s , x ( s ) ) d s + α ( t ) H ( max 0 u t x ( u ) ) + β ( t ) L t 0 ( x )
文摘本文在一些合适的条件下,我们证明强解的存在和唯一性的摄动随机微分方程反映边界(PSDERB) , { x⁢(t ) = x⁢(0)+∫0 tσ⁢(x⁢(年代 ) ) ⁢ d B⁢(s ) + ∫0 t b⁢(x⁢(年代 ) ) ⁢ d s +α⁢(t)⁢H⁢u (max 0≤≤t⁡x⁢(u ) ) + β⁢(t)⁢L t 0⁢(x)x⁢(t ) 所有⁢≥0 t≥0 , 左{{对齐}{}开始x (t)和= x (0) + int_ {0} ^ {t} σ(年代,x (s)) , dB (s) + int_ {0} ^ {t} b (s, x (s)) d + α(t) H bigl {(} max_ {0 leq u leq t} x (u) bigr{)} + β(t) L_ {t} ^ {0} (x) x (t)和 组0 四文本所有}{ t 组0 {对齐}正确的结束。其中𝐻为连续的r值函数,σ,b, α sigma,b, α alpha,和时延为可测函数,L t 0 L_{t}^{0}表示半鞅变量的时间在零点处的局部时间。
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引用次数: 0
A weight Monte Carlo estimation of fluctuations in branching processes 分支过程波动的权值蒙特卡罗估计
Q4 Mathematics Pub Date : 2023-10-24 DOI: 10.1515/mcma-2023-2015
Vladimir Uchaikin, Elena Kozhemiakina
Abstract It is well known that shortened modeling of particle trajectories with the use multiplicative statistical weights, as a rule, increases the efficiency of the program (in terms of accuracy/time ratio). This trick is often used in non-branching schemes simulating transfer processes without multiplication (for example, the transfer of X-ray radiation), in which it is sufficient to confine ourselves to studying only the average values of the field characteristics. With an increase in energy, however, multiplication processes begin to play a significant role (the production of electron-photon pairs by gamma quanta with energies above 1.022 MeV, etc.), when the resulting trajectory is not just a broken curve in the phase space, but a branched tree. This technique is also applicable to this process, but only if the study of statistical fluctuations and correlations is not the purpose of the calculation. The present review contains the basic concepts of the Monte Carlo method as applied to the theory of particle transport, demonstration of the weighting method in non-branching processes, and ends with a discussion of unbiased estimates of the second moment and covariance of additive functionals.
摘要:众所周知,使用乘法统计权值来缩短粒子轨迹建模,通常会提高程序的效率(在精度/时间比方面)。这种技巧通常用于模拟没有乘法的转移过程的非分支方案(例如,x射线辐射的转移),在这种情况下,我们只研究场特征的平均值就足够了。然而,随着能量的增加,倍增过程开始发挥重要作用(能量高于1.022 MeV的伽马量子产生电子-光子对等),此时产生的轨迹不仅仅是相空间中的断裂曲线,而是分支树。这种技术也适用于这一过程,但前提是研究统计波动和相关性不是计算的目的。本文综述了应用于粒子输运理论的蒙特卡罗方法的基本概念,证明了非分支过程中的加权方法,最后讨论了加性泛函的二阶矩和协方差的无偏估计。
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引用次数: 0
Option pricing: Examples and open problems 期权定价:例子和悬而未决的问题
Q4 Mathematics Pub Date : 2023-10-24 DOI: 10.1515/mcma-2023-2014
Nikolaos Halidias
Abstract There is no method of predicting the price of an option other than hedging strategies such as the binomial hedging strategy, the Black–Scholes hedging strategy and others. We will study these two basic hedging strategies in terms of their feasibility, and we will see that the Black–Scholes hedging strategy is not feasible because this strategy demands instantaneously rebuilding the replicating portfolio. Consequently, the real world prices of the options are not relevant at all with the Black–Scholes hedging strategy! We will suitably redefine the binomial hedging strategy so that it will be practically useful and present other feasible and generally more effective hedging strategies with some of them practically useful for options with no tradable underlying assets. Finally, we will mention some open questions related to the above.
摘要期权价格预测除了套期保值策略,如二项套期保值策略、布莱克-斯科尔斯套期保值策略等,没有其他方法。我们将研究这两种基本对冲策略的可行性,我们将看到布莱克-斯科尔斯对冲策略不可行,因为该策略需要立即重建复制投资组合。因此,期权的真实世界价格与布莱克-斯科尔斯对冲策略完全无关!我们将适当地重新定义二项对冲策略,使其在实际中有用,并提出其他可行且通常更有效的对冲策略,其中一些策略对没有可交易标的资产的期权实际有用。最后,我们将提到与上述相关的一些悬而未决的问题。
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引用次数: 0
Analysis of wall-modelled particle/mesh PDF methods for turbulent parietal flows 紊流壁面模拟颗粒/网格PDF方法分析
Q4 Mathematics Pub Date : 2023-10-19 DOI: 10.1515/mcma-2023-2017
Guilhem Balvet, Jean-Pierre Minier, Yelva Roustan, Martin Ferrand
Abstract Lagrangian stochastic methods are widely used to model turbulent flows. Scarce consideration has, however, been devoted to the treatment of the near-wall region and to the formulation of a proper wall-boundary condition. With respect to this issue, the main purpose of this paper is to present an in-depth analysis of such flows when relying on particle/mesh formulations of the probability density function (PDF) model. This is translated into three objectives. The first objective is to assess the existing an-elastic wall-boundary condition and present new validation results. The second objective is to analyse the impact of the interpolation of the mean fields at particle positions on their dynamics. The third objective is to investigate the spatial error affecting covariance estimators when they are extracted on coarse volumes. All these developments allow to ascertain that the key dynamical statistics of wall-bounded flows are properly captured even for coarse spatial resolutions.
拉格朗日随机方法被广泛应用于紊流模型。然而,很少考虑到近壁区域的处理和适当的壁-边界条件的制定。关于这个问题,本文的主要目的是在依赖概率密度函数(PDF)模型的粒子/网格公式时对这种流动进行深入分析。这可以转化为三个目标。第一个目标是评估现有的非弹性壁面边界条件,并提出新的验证结果。第二个目标是分析平均场在粒子位置的插值对其动力学的影响。第三个目标是研究在粗体积上提取协方差估计时空间误差对协方差估计的影响。所有这些发展都可以确定,即使在粗糙的空间分辨率下,也可以适当地捕获有壁流动的关键动态统计数据。
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引用次数: 0
A wavelet-based method in aggregated functional data analysis 基于小波的聚合功能数据分析方法
Q4 Mathematics Pub Date : 2023-10-14 DOI: 10.1515/mcma-2023-2016
Alex Rodrigo dos Santos Sousa
Abstract In this paper, we consider aggregated functional data composed by a linear combination of component curves and the problem of estimating these component curves. We propose the application of a bayesian wavelet shrinkage rule based on a mixture of a point mass function at zero and the logistic distribution as prior to wavelet coefficients to estimate mean curves of components. This procedure has the advantage of estimating component functions with important local characteristics such as discontinuities, spikes and oscillations for example, due the features of wavelet basis expansion of functions. Simulation studies were done to evaluate the performance of the proposed method, and its results are compared with a spline-based method. An application on the so-called Tecator dataset is also provided.
摘要本文考虑由线性组合的分量曲线组成的聚合函数数据,以及这些分量曲线的估计问题。我们提出了一种基于零点质量函数和小波系数前的logistic分布混合的贝叶斯小波收缩规则的应用,以估计分量的平均曲线。由于函数的小波基展开性,该方法具有估计具有重要局部特征(如不连续、尖峰和振荡)的分量函数的优点。仿真研究了该方法的性能,并将其结果与基于样条的方法进行了比较。还提供了一个关于所谓的Tecator数据集的应用程序。
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引用次数: 1
Randomized vector iterative linear solvers of high precision for large dense system 大型密集系统高精度随机向量迭代线性求解器
Q4 Mathematics Pub Date : 2023-10-04 DOI: 10.1515/mcma-2023-2013
Karl K. Sabelfeld, Anastasiya Kireeva
Abstract In this paper we suggest randomized linear solvers with a focus on refinement issue to achieve a high precision while maintaining all the advantages of the Monte Carlo method for solving systems of large dimension with dense matrices. It is shown that each iterative refinement step reduces the error by one order of magnitude. The crucial point of the suggested method is, in contrast to the standard Monte Carlo method, that the randomized vector algorithm computes the entire solution column at once, rather than a single component. This makes it possible to efficiently construct the iterative refinement method. We apply the developed method for solving a system of elasticity equations.
在本文中,我们提出了随机线性求解器,重点是细化问题,以实现高精度,同时保持蒙特卡罗方法在求解具有密集矩阵的大维系统时的所有优点。结果表明,每个迭代细化步骤减小误差的数量级。与标准蒙特卡罗方法相比,所建议的方法的关键点是随机向量算法一次计算整个解列,而不是单个分量。这使得有效地构造迭代细化方法成为可能。我们应用所开发的方法来求解弹性方程组。
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引用次数: 0
Frontmatter 头版头条
Q4 Mathematics Pub Date : 2023-09-01 DOI: 10.1515/mcma-2023-frontmatter3
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引用次数: 0
On the stationarity and existence of moments of the periodic EGARCH process 关于周期EGARCH过程的平稳性和矩的存在性
IF 0.9 Q4 Mathematics Pub Date : 2023-08-01 DOI: 10.1515/mcma-2023-2011
Ines Lescheb, Walid Slimani
Abstract In this paper, we will consider periodic EGARCH ⁡ ( p , p ) {operatorname{EGARCH}(p,p)} (exponential generalized autoregressive conditional heteroscedastic) processes denoted by PEGARCH ⁡ ( p , p ) {operatorname{PEGARCH}(p,p)} . These processes are similar to the standard EGARCH processes, but include seasonally varying coefficients. We examine the probabilistic structure of an EGARCH-type stochastic difference equation with periodically-varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions (in a periodic sense) based on a Markovian representation. The closed forms of higher moments are, under these conditions, established. Furthermore, the expressions for the Kurtosis coefficient and the autocorrelations of squared observations are derived. The general theory is illustrated by considering special cases such as the symmetric and the asymmetric cases of the second order PEGARCH model.
本文将考虑周期EGARCH (p,p) {operatorname{EGARCH}(p,p)}(指数广义自回归条件异方差)过程,表示为PEGARCH (p,p) {operatorname{PEGARCH}(p,p)}。这些过程类似于标准EGARCH过程,但包括季节变化的系数。研究了一类参数周期性变化的egarch型随机差分方程的概率结构。基于马尔可夫表示,给出了周期平稳解存在的充分必要条件。在这些条件下,高矩的封闭形式就确立了。此外,还推导了峰度系数和平方观测值的自相关表达式。通过考虑二阶PEGARCH模型的对称和非对称情况来说明一般理论。
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引用次数: 0
期刊
Monte Carlo Methods and Applications
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