Minimizing the Variance of a Mathematical Expectation Estimate for a Diffusion Process Functional Based on a Parametric Transformation of a Parabolic Boundary Value Problem

S. A. Gusev

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Minimizing the Variance of a Mathematical Expectation Estimate for a Diffusion Process Functional Based on a Parametric Transformation of a Parabolic Boundary Value Problem

机译：基于抛物型边值问题的参数变换，使扩散过程函数的数学期望估计值的方差最小

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This paper deals with finding ways of reducing the variance of a mathematical expectation estimate for the functional of a diffusion process moving in a domain with an absorbing boundary. The estimate of mathematical expectation of the functional is obtained based on a numerical solution of stochastic differential equations (SDEs) by using the Euler method. A formula of the limiting variance is derived with decreasing integration step in the Euler method. A method of reducing the variance value of the estimate based on transformation of the parabolic boundary value problem corresponding to the diffusion process is proposed. Some numerical results are presented.

机译：本文探讨了减少数学期望估计值方差的方法，这些期望值对于具有吸收边界的域中移动的扩散过程的功能而言。使用Euler方法，基于随机微分方程（SDE）的数值解，可以获得对该函数的数学期望的估计。在欧拉方法中，随着积分步长的减小，得出了极限方差的公式。提出了一种基于与扩散过程相对应的抛物线型边值问题的变换来减小估计方差值的方法。给出了一些数值结果。

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《Numerical analysis and applications》 |2011年第2期|共11页
作者
S. A. Gusev;
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正文语种 eng
中图分类应用数学;
关键词
diffusion process; stochastic differential equations; absorbing boundary; variance of functional estimate; Euler method;

机译：扩散过程随机微分方程吸收边界估计函数的方差欧拉法;

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1. Minimizing the Variance of a Mathematical Expectation Estimate for a Diffusion Process Functional Based on a Parametric Transformation of a Parabolic Boundary Value Problem [J] . S. A. Gusev Numerical analysis and applications . 2011,第2期

机译：基于抛物型边值问题的参数变换，使扩散过程函数的数学期望估计值的方差最小
2. Modelling of high-dimensional diffusion stochastic process with nonlinear coefficients for engineering applications-part I: approximations for expectation and variance of nonstationary process [J] . Y. V. Mamontov, M. Willander, T. Lewin Mathematical models and methods in applied sciences . 1999,第8期

机译：工程应用非线性系数的高维扩散随机过程建模-第一部分：非平稳过程的期望和方差的近似值
3. Explicit representations for the expectations of exponential functionals of the multi-factor variance gamma process and their applications [J] . Ivanov Roman V., Ano Katsunori Stochastics: An International Journal of Probability and Stochastic Processes . 2016,第1a4期

机译：明确表示期望的多因素方差伽玛过程的指数函数及其应用
4. NUCLEATION ON IRRATIONAL INTERPHASE BOUNDARIES IN DIFFUSIONAL PHASE TRANSFORMATIONS OF STEELS [C] . T. Furuhara, G. Miyamoto, H. Saito, International Conference on Solid - Solid Phase Transformations in Inorganic Materials 2005 vol.1; 20050529-0603; Phoenix,AZ(US) . 2005

机译：钢的扩散相变中不合理相间边界的成核
5. FUNCTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS: MATHEMATICAL THEORY OF NONLINEAR PARABOLIC SYSTEMS WITH APPLICATIONS IN FIELD THEORY AND STATISTICAL MECHANICS. [D] . DOERING, CHARLES ROGERS. 1985

机译：功能随机微分方程：非线性抛物方程组的数学理论及其在场论和统计力学中的应用。
6. Self-similar intermediate asymptotics for nonlinear degenerate parabolic free-boundary problems that occur in image processing [O] . G. I. Barenblatt 2001

机译：非线性退化的抛物线形自由边界问题在图像处理中的自相似中间渐近性
7. Approximation of Expectation of Diffusion Processes based on Lie Algebra and Malliavin Calculus (Mathematical Economics) [O] . Kusuoka Shigeo 2003

机译：基于李代数和Malliavin微积分的扩散过程的期望逼近（数学经济学）
8. Minimizing a Project Cost with Bounds on the Expectation and Variance of the Delay Time. [R] . Falk, J. E. 1978

机译：最大限度地降低项目成本的期限和延迟时间的变化。

Minimizing the Variance of a Mathematical Expectation Estimate for a Diffusion Process Functional Based on a Parametric Transformation of a Parabolic Boundary Value Problem

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