作为提供内稳态的随机方法的最大和最小过程的逼近

IF 0.3 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
G. Beliavsky, N. Danilova, G. Ougolnitsky
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引用次数: 0

摘要

我们考虑了平稳扩散过程轨迹的有界泛函的计算。由于不存在这个问题的解析解,因此有必要使用数值方法。采用蒙特卡罗(MC)方法是获得数值方法的一个可能方向。这包括再现一个随机过程的轨迹,随后对轨迹进行平均。为了简化轨迹的再现,本文采用了吉尔萨诺夫变换。主要目标是近似上限和最小过程,与经典方法相比,这使我们能够更准确地计算函数的数学期望,这取决于时间间隔结束时的上限和最小过程的值。该方法是通过停止Wiener过程的多次通道,随机划分时间轴的间隔,近似密度代替测度,使用MC方法计算期望。该方法的应用之一是在给定区域内保持随机过程的稳态问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximation of supremum and infimum processes as a stochastic approach to the providing of homeostasis
We consider the calculation of bounded functional of the trajectories of a stationary diffusion process. Since an analytical solution to this problem does not exist, it is necessary to use numerical methods. One possible direction for obtaining the numerical method is applying the Monte Carlo (MC) method. This involves reproducing the trajectory of a random process with subsequent averaging over the trajectories. To simplify the reproduction of the trajectory, the Girsanov transform is used in this paper. The main goal is to approximate the supremum and infimum processes, which allows us to more accurately compute the mathematical expectation of a function depending on the values of the supremum and infimum processes at the end of the time interval compared to the classical method. The method is based on randomly dividing the interval of the time axis by stopping times passages of the Wiener process, approximating the density to replace the measure, and using the MC method to calculate the expectation. One of the applications of the method is the task of keeping a random process in a given area the problem of homeostasis.
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来源期刊
CiteScore
1.30
自引率
50.00%
发文量
10
期刊介绍: The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.
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