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Asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system 非对称核方法在 PH/M/1 排队系统强稳定性研究中的应用
IF 0.9 Q3 STATISTICS & PROBABILITY Pub Date : 2023-12-13 DOI: 10.1515/mcma-2023-2023
Yasmina Djabali, Sedda Hakmi, Nabil Zougab, D. Aïssani
Abstract This paper proposes the nonparametric asymmetric kernel method in the study of strong stability of the PH/M/1 queuing system, after perturbation of arrival distribution to evaluate the proximity of the complex GI/M/1 system, where GI is a unknown general distribution. The class of generalized gamma (GG) kernels is considered because of its several interesting properties and flexibility. A simulation for several models illustrates the performance of the GG asymmetric kernel estimators in the study of strong stability of the PH/M/1, by computing the variation distance and the stability error.
摘要本文提出了非参数非对称核方法,用于研究PH/M/1排队系统的强稳定性,在到达分布扰动后评价复杂GI/M/1系统的接近性,其中GI是一个未知的一般分布。广义伽玛核(GG)类由于其几个有趣的性质和灵活性而被考虑。通过计算变异距离和稳定性误差,对多个模型进行了仿真,验证了GG非对称核估计在PH/M/1强稳定性研究中的性能。
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引用次数: 0
Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations 球上随机游走法求解各向异性瞬态扩散问题及通量计算
Q3 STATISTICS & PROBABILITY Pub Date : 2023-11-15 DOI: 10.1515/mcma-2023-2022
Irina Shalimova, Karl Sabelfeld
Abstract The Random Walk on Spheres (RWS) algorithm for solving anisotropic transient diffusion problems based on a stochastic learning procedure for calculation of the exit position of the anisotropic diffusion process on a sphere is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have numerically calculated the probability density for the exit position on a sphere. The first passage time is then represented explicitly. The method can easily be implemented to solve diffusion problems with spatially varying diffusion coefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation where the measured functions are the exciton fluxes to the semiconductor’s substrate and on the dislocation surface.
提出了一种求解各向异性瞬态扩散问题的随机学习算法(RWS),该算法用于计算各向异性扩散过程在球体上的出口位置。将球上随机游走法直接推广到各向异性扩散方程是不可能的,因此,我们数值计算了球上出口位置的概率密度。然后显式地表示第一个通过时间。该方法可方便地求解复杂三维区域中具有空间变化扩散系数的扩散问题。粒子跟踪算法对于边界通量的计算具有很高的效率。我们将开发的算法应用于解决具有螺纹位错的半导体材料中的激子输运,其中测量的函数是半导体衬底和位错表面上的激子通量。
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引用次数: 0
On the estimation of periodic signals in the diffusion process using a high-frequency scheme 用高频方法估计扩散过程中的周期信号
Q3 STATISTICS & PROBABILITY Pub Date : 2023-11-11 DOI: 10.1515/mcma-2023-2020
Getut Pramesti, Ristu Saptono
Abstract The estimation of the frequency component is very interesting to study, considering its unique nature when these parameters are together in their amplitude. The periodicity of the frequency components is also thought to affect the convergence of these parameters. In this paper, we consider the problem of estimating the frequency component of a periodic continuous-time sinusoidal signal. Under the high-frequency sampling setting, we provide the frequency components’ consistency and asymptotic normality. It is observed that the convergence rate of the continuous-time sinusoidal signal of the diffusion process is the same as the continuous-time sinusoidal signal of the Ornstein–Uhlenbeck process, which is mentioned in [G. Pramesti, Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process, Monte Carlo Methods Appl. 29 (2023), 1, 1–32]. The result of this study deduces that the convergence rate of the frequency is the same as long as the signal is periodic. In this case, the existence of the rate of reversion does not affect the convergence rate of the frequency components. Further, the result of the study, that is, the convergence rate of the frequency is ( n h ) 3 sqrt{(nh)^{3}} , also revised the previous one in [G. Pramesti, The least-squares estimator of sinusoidal signal of diffusion process for discrete observations, J. Math. Comput. Sci. 11 (2021), 5, 6433–6443], which mentioned ( n h ) 3 h sqrt{(nh)^{3}h} . The proposed approach is demonstrated with a ten-minute sampling rate of real data on the energy consumption of light fixtures in one Belgium household.
频率分量的估计是一个非常有趣的研究,因为当这些参数在其幅值中同时存在时,频率分量的估计具有独特的性质。频率分量的周期性也被认为会影响这些参数的收敛性。本文研究了周期连续正弦信号的频率分量估计问题。在高频采样设置下,给出了频率分量的一致性和渐近正态性。可以观察到扩散过程的连续时间正弦信号的收敛速度与Ornstein-Uhlenbeck过程的连续时间正弦信号的收敛速度相同,这在[G]中提到。[2]张志强,时间非齐次Ornstein-Uhlenbeck过程参数最小二乘估计,蒙特卡罗方法应用,29(2023),1 - 32。本文的研究结果表明,只要信号是周期性的,频率的收敛速度是相同的。在这种情况下,反转速率的存在并不影响频率分量的收敛速率。进一步,研究的结果,即频率的收敛速率为(n¹h) 3 sqrt{(nh)^{3}},也修正了先前[G]中的结果。李志强,离散观测扩散过程中正弦信号的最小二乘估计,数学学报。第一版。科学通报,11(2021),5,6433-6443],其中提到了(n减去h) 3减去h sqrt{(nh)^{3}h}。该方法通过对比利时一户家庭灯具能耗的10分钟采样率的实际数据进行了验证。
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引用次数: 0
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
Q3 STATISTICS & PROBABILITY 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
Q3 STATISTICS & PROBABILITY 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
Q3 STATISTICS & PROBABILITY 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, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>{</m:mo> <m:mtable columnspacing="0pt" displaystyle="true" rowspacing="0pt"> <m:mtr> <m:mtd columnalign="right"> <m:mrow> <m:mi>x</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:mtd> <m:mtd columnalign="left"> <m:mrow> <m:mrow> <m:mi /> <m:mo>=</m:mo> <m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mn>0</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo rspace="0.055em">+</m:mo> <m:mrow> <m:msubsup> <m:mo>∫</m:mo> <m:mn>0</m:mn> <m:mi>t</m:mi> </m:msubsup> <m:mrow> <m:mi>σ</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>s</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo lspace="0.170em">⁢</m:mo> <m:mrow> <m:mo mathvariant="italic" rspace="0em">d</m:mo> <m:mi>B</m:mi> </m:mrow> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>s</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo rspace="0.055em">+</m:mo> <m:mrow> <m:msubsup> <m:mo>∫</m:mo> <m:mn>0</m:mn> <m:mi>t</m:mi> </m:msubsup> <m:mrow> <m:mi>b</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>s</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo lspace="0.170em">⁢</m:mo> <m:mrow> <m:mo mathvariant="italic" rspace="0em">d</m:mo> <m:mi>s</m:mi> </m:mrow> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>α</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>⁢</m:mo> <m:mi>H</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo maxsize="120%" minsize="120%">(</m:mo> <m:mrow> <m:mrow> <m:munder> <m:mi>max</m:mi> <m:mrow> <m:mn>0</m:mn> <m:mo>≤</m:mo> <m:mi>u</m:mi> <m:mo>≤</m:mo> <m:mi>t</m:mi> </m:mrow> </m:munder> <m:mo lspace="0.167em">⁡</m:mo> <m:mi>x</m:mi> </m:mrow> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>u</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo maxsize="120%" minsize="120%">)</m:mo> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>β</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>t</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>⁢</m:mo> <m:msubsup> <m:mi>L</m:mi> <m:mi>t</m:mi> <m:mn>0</m:mn> </m:msubsup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:mrow>
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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&lt;m:mrow&gt; &lt;m:mi /&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo rspace=\"0.055em\"&gt;+&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msubsup&gt; &lt;m:mo&gt;∫&lt;/m:mo&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;/m:msubsup&gt; &lt;m:mrow&gt; &lt;m:mi&gt;σ&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;s&lt;/m:mi&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;s&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo lspace=\"0.170em\"&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo mathvariant=\"italic\" rspace=\"0em\"&gt;d&lt;/m:mo&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;s&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo rspace=\"0.055em\"&gt;+&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msubsup&gt; &lt;m:mo&gt;∫&lt;/m:mo&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;/m:msubsup&gt; &lt;m:mrow&gt; &lt;m:mi&gt;b&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;s&lt;/m:mi&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;s&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo lspace=\"0.170em\"&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo mathvariant=\"italic\" rspace=\"0em\"&gt;d&lt;/m:mo&gt; &lt;m:mi&gt;s&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;α&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;H&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo maxsize=\"120%\" minsize=\"120%\"&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mrow&gt; &lt;m:munder&gt; &lt;m:mi&gt;max&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;m:mo&gt;≤&lt;/m:mo&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;m:mo&gt;≤&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:munder&gt; &lt;m:mo lspace=\"0.167em\"&gt;⁡&lt;/m:mo&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo maxsize=\"120%\" minsize=\"120%\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;β&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:msubsup&gt; &lt;m:mi&gt;L&lt;/m:mi&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;/m:msubsup&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;x&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; ","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"36 1-2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Q3 STATISTICS & PROBABILITY 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
Q3 STATISTICS & PROBABILITY 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
Q3 STATISTICS & PROBABILITY 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
Q3 STATISTICS & PROBABILITY 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
期刊
Monte Carlo Methods and Applications
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