MODELLING OF HIGH-DIMENSIONAL DIFFUSION STOCHASTIC PROCESS WITH NONLINEAR COEFFICIENTS FOR ENGINEERING APPLICATIONS — PART I: APPROXIMATIONS FOR EXPECTATION AND VARIANCE OF NONSTATIONARY PROCESS

Author:

MAMONTOV Y. V.12,WILLANDER M.1,LEWIN T.2

Affiliation:

1. Laboratory of Physical Electronics and Photonics, School of Physics and Engineering Physics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden

2. Core Unit Research Center, Microwave and High-Speed Electronics, Ericsson Microwave Systems AB, S-431 84 Mölndal, Sweden

Abstract

This work is devoted to diffusion stochastic processes (DSPs) with nonlinear coefficients in n-dimensional Euclidean space at high n (n is much greater than a few units). It deals with expectation and variance of a nonstationary process whereas our accompanying work deals with covariance and spectral density of a stationary process. Combined, analytical-numerical approach is a reasonable and perhaps the only way to treat high-dimensional DSPs in practice. Each of the above works develops the corresponding parts of the analytical basis for this combined treatment. The present work proposes approximate analytical expressions for the expectation and variance in the form of two ordinary differential equation (ODE) systems. They are derived within DSP theory without any techniques directly related to stochastic differential equations. Both ODE systems allow for space nonhomogeneities of the diffusion and damping matrixes and thereby do take nonlinearities of the DSP coefficients into account. Some related topics like invariant processes and the aspects of practical implementation of the above expressions are discussed as well. A proper attention is paid to formulation of some features important in applications of DSPs to the real-world problems. The results of this work can equally be used in various engineering fields.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3