数学建模中的随机积分和微分方程 Stochastic Integral And Differential Equations In Mathematical Modelling
基本信息
Publisher：WSPC (EUROPE) (April 27, 2023)
Language：English
Hardcover：318 pages
ISBN-10：1800613571
ISBN-13：978-1800613577
Item Weight：1.31 pounds
Dimensions：6 x 0.94 x 9 inches
页面参数仅供参考，具体以实物为准
书籍简介
用微分方程对系统进行建模，通常要求所涉及的参数是完全已知的。这类模型往往源于物理学或经济学中的问题，在这些问题中我们没有足够的参数值信息。一类重要的随机数学模型是随机偏微分方程（SPDEs），它可以被看作是具有有限或无限维度随机过程的确定性偏微分方程（PDEs）--要么有彩色噪声，要么有白噪声。虽然白噪声是一种纯粹的数学构造，但它可以成为快速随机波动的良好模型。
数学建模中的随机积分和微分方程涉及到由维纳过程驱动的随机微分方程（SDE）的离散时间近似的分析。它还提供了处理SDE和随机过程的理论基础。
本书以简单明了的数学逻辑语言编写，从一开始就提供了关于随机微积分的基本定义和定理。每一章都有通过图和表的说明性例子。读者还可以通过使用书中介绍的程序构建新的小波。数学建模中的随机积分和微分方程》满足了现有文献中对这一主题领域的全面描述的空白。
The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes — either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.
Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes.
This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.
作者简介
桑塔努-萨哈-雷博士目前是印度鲁尔克拉国家技术学院数学系的教授和前主任。萨哈-雷博士于2008年在印度加尔各答的贾达夫布尔大学完成博士学位。他于2001年在印度Shibpur的印度工程科学与技术学院（IIEST）（前身为孟加拉工程学院）获得MCA（计算机应用硕士）学位。他于1998年在印度加尔各答的加尔各答大学完成了应用数学的硕士学位，并于1996年在印度加尔各答的圣泽维尔学院（现名为加尔各答圣泽维尔大学）完成了数学学士（荣誉）学位。2018年，他被选为英国数学及其应用研究所的研究员。
斯坦福大学与出版社Elsevier和SciTech Strategies一起，发布了一份世界各领域前2%科学家的报告。萨哈-雷博士被斯坦福大学列入世界前2%的科学家名单，该名单近期发布，并发表在开放的科学杂志PLoS（公共科学图书馆）上。在印度，萨哈-雷博士在 "数值和计算数学 "领域排名前列，其相应的世界排名为107。根据John PA Ioannidis博士领导的斯坦福大学科学家团队进行的学科分析，他在印度令人羡慕的 "世界前2%科学家排名 "名单中名列前茅。斯坦福大学在各个领域的世界前2%科学家的新名单中包括了1000多名来自印度的科学家。近期，他被正式选为美国科学研究荣誉协会Sigma Xi的正式成员。
萨哈-雷博士有超过21年的本科和研究生教学经验，他曾在鲁尔克拉国家技术学院和西孟加拉邦加尔各答的两所知名私立工程学院任教。他在应用数学的各个领域有超过20年的研究经验。他在众多领域和各种国际知名的SCI期刊上发表了许多经同行评议的研究论文。关于详细的引文概况，读者可以参考Scopus。迄今为止，他在国际知名期刊上发表了222多篇研究论文，其中包括191多篇SCI期刊论文。在过去三年（2015年至2017年）中，他在整个IOP Publishing组合中发表的物理学领域，利用Web of Science中记录的引文，被授予2018年印度IOP Publishing高引文作者奖。
他独自撰写了一本题为《图论与算法及其应用：应用科学与技术》的书，由Springer出版。独著的《分数微积分与核反应堆动力学应用》一书已由CRC出版社的Taylor & Francis集团出版。另一本题为《Numerica》的独著
Dr Santanu Saha Ray is currently a Professor and Former Head of the Department of Mathematics, National Institute of Technology, Rourkela, India. Dr Saha Ray completed his PhD in 2008 from Jadavpur University, Kolkata, India. He received his MCA (Master of Computer Applications) degree in 2001 from the Indian Institute of Engineering Science and Technology (IIEST), erstwhile Bengal Engineering College, Shibpur, India. He completed a master's degree in applied mathematics at Calcutta University, Kolkata, India, in 1998 and a bachelor's (honours) degree in mathematics at St. Xavier's College(currently known as St. Xavier's University, Kolkata), Kolkata, India, in 1996. He was elected Fellow of the Institute of Mathematics and Its Applications, United Kingdom, in 2018.
Stanford University together with the publishing house Elsevier and SciTech Strategies, has released a report of the top 2% best scientists in the World in various fields. Dr Saha Ray is enlisted in the World's Top 2% Scientists List by Stanford University, which was released recently and published in the open access Science journal PLoS (Public Library of Science). In India, Dr Saha Ray is in No. 1 position in the field of "Numerical and Computational Mathematics" and his corresponding World Ranking is 107. He is at the top of the most coveted list of "WORLD RANKING OF TOP 2% SCIENTISTS" from India as per a subject-wise analysis conducted by a team of scientists at Stanford University, led by Dr John PA Ioannidis. Stanford University's new list of the top 2% scientists in the world in various fields includes over 1000 scientists from India. Recently, he was duly elected for Full Membership in Sigma Xi, The Scientific Research Honor Society, USA.
Dr Saha Ray has more than 21 years of teaching experience at the undergraduate and postgraduate levels in glorious Institutes like National Institute of Technology, Rourkela and two renowned private Engineering Institutes in Kolkata, West Bengal. He has more than 20 years of research experience in various fields of Applied Mathematics. He has published many peer-reviewed research papers in numerous fields and various international SCI journals of repute. For a detailed citation overview, the reader may be referred to Scopus. To date, he has more than 222 research papers published in journals of international repute, including more than 191 SCI journal papers. He was awarded an IOP Publishing Top Cited Author Award 2018 from India in the field of Physics published across the whole IOP Publishing portfolio in the past three years (2015 to 2017), using citations recorded in Web of Science.
He has solely authored a book entitled Graph Theory with Algorithms and Its Applications: in Applied Science and Technology published by Springer. A solely authored book entitled Fractional Calculus with Applications for Nuclear Reactor Dynamics has been published by the CRC Press of the Taylor & Francis Group. Another solely authored book entitled Numerical Analysis with Algorithms and Programming has been also published in CRC Press of Taylor & Francis Group, USA. Another three books entitled Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations, Generalized Fractional Order Differential Equations Arising in Physical Models and Novel Methods for Solving Linear and Nonlinear Integral Equations have been published by CRC Press of Taylor & Francis Group, USA. Recently his book entitled Nonlinear Differential Equations in Physics has been launched by Springer Nature.
Currently, he is acting as editor-in-chief for the Springer Scopus international journal entitled International Journal of Applied and Computational Mathematics. He is also an associate editor of a Springer SCIE international journal Mathematical Sciences and reviewer of several journals of Elsevier, Springer and Taylor and Francis, etc. He was also been the lead guest editor in the International SCI journals of Hindawi Publishing Corporation, USA.
He has contributed papers on several topics, such as fractional calculus, mathematical modelling, mathematical physics, stochastic modelling, integral equations, and wavelet methods. He is a member of the Society for Industrial and Applied Mathematics (SIAM) and the American Mathematical Society (AMS).
目录
Preface
About the Author
List of Figures
Index
Introduction and Preliminaries of Stochastic Calculus
Analytical Solutions of Stochastic Differential Equations
Numerical Solutions of Stochastic Integral Equation
Numerical Solutions of Multidimensional Stochastic Integral Equation
Numerical Solutions of Stochastic Integral Equations with Fractional Brownian Motion
Numerical Solutions of Stochastic Differential Equations Arising in Physical Phenomena
Numerical Solutions of Stochastic Point Kinetics Equations
Numerical Solutions of Fractional Stochastic Point Kinetics Equation
Conclusions and Future Directions
References
Index
