逻辑随机微分方程的近似矩函数

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED
Coşkun Çetin, Jasmina Đorđević
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引用次数: 0

摘要

本文介绍了逻辑随机微分方程矩函数的连续逼近方法。我们首先将相应的矩函数系统简化为线性常微分方程的无限系统。然后,我们确定矩函数的某些上界和下界,并利用这些界值通过适当的截断、迭代和局部改进步骤近似求解所得到的系统。在获得关于误差规范的一些一般理论结果并描述了逻辑 SDE 的一般算法之后,我们将重点放在数值实现中的随机 Verhulst 系统上。我们将其矩近似值与基于模拟的数值解法进行了比较,后者包括路径解的离散化以及其他收敛数值程序,如半隐式分步欧拉方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Approximate moment functions for logistic stochastic differentialequations

Approximate moment functions for logistic stochastic differentialequations

In this paper, we introduce a method of successive approximations for moment functions of logistic stochastic differential equations. We first reduce the system of the corresponding moment functions to an infinite system of linear ordinary differential equations. Then, we determine certain upper and lower bounds on the moment functions, and utilize these bounds to solve the resulting systems approximately via suitable truncations, iterations and a local improvement step. After obtaining some general theoretical results on the error norms and describing a general algorithm for logistic SDE, we focus on stochastic Verhulst systems in numerical implementations. We compare their moment approximations with numerical solutions via simulation-based methods that include discretizations of the pathwise solutions as well as other convergent numerical procedures like semi-implicit split-step Euler methods.

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来源期刊
Numerical Algorithms
Numerical Algorithms 数学-应用数学
CiteScore
4.00
自引率
9.50%
发文量
201
审稿时长
9 months
期刊介绍: The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.
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