Brownian Motion: Elements, Dynamics and Applications

Mark A. McKibben, PhD (Editor)
West Chester University, West Chester, PA, USA

Micah Webster (Editor)
Department of Mathematics and Computer Science, Goucher College, Baltimore, MD, USA

Series: Mathematics Research Developments, Physics Research and Technology
BISAC: MAT000000

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$280.00

Volume 10

Issue 1

Volume 2

Volume 3

Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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The fields of study in which random fluctuations arise and cannot be ignored are as disparate and numerous as there are synonyms for the word “noise.” In the nearly two centuries following the discovery of what has come to be known as Brownian motion, named in homage to botanist Robert Brown, scientists, engineers, financial analysts, mathematicians, and literary authors have posited theories, created models, and composed literary works which have accounted for environmental noise.

This volume offers a glimpse into the ways in which Brownian motion has crept into a myriad of fields of study through fifteen distinct chapters written by mathematicians, physicists, and other scholars. The intent is to especially highlight the vastness of scholarly work that explains various facets of Nature made possible by one scientist’s curiosity sparked by observing sporadic movement of specks of pollen under a microscope in a 19th century laboratory.
(Imprint: Nova)

Preface
pp. vii-ix

Chapter 1
Stochastic Modelling and Simulations of Structured Investment Plans
(Ling Feng, Yile Li, Xuerong Mao, and Zhigang Huang, School of Economics and Management, Fuzhou University, Fuzhou, China, and others)
pp. 1-22

Chapter 2
Limitation of the Least Square Method in the Evaluation of Dimension of Fractal Brownian Motions
(Siming Liu and Bingqiang Qiao, Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China, and others)
pp. 23-36

Chapter 3
Parameter Estimation for Weighted Fractional Ornstein-Uhlenbeck Processes with Discrete Observations
(Xiuwei Yin, Guangjun Shen, and Longjuan Deng, Anhui Normal University, Wuhu, China)
pp. 37-52

Chapter 4
Comparing Traditional Proofs of the Modulus of Continuity and the Law of the Iterated Logarithm to a New Method which Yields Rates of Convergence
(Lisa Marano, West Chester University, Pennsylvania, USA)
pp. 53-74

Chapter 5
Transporting a Macroscopic Object by Brownian Motion — An Object as a Pollen Particle, Robots as Liquid Molecules
(Teturo Itami, Robotics Industry Development Council, Japan)
pp. 75-100

Chapter 6
Maximum Principle for Stochastic Discrete-Time Ito Equations
(N. I. Mahmudov, Eastern Mediterranean University Gazimagusa, TRNC Mersin, Turkey)
pp. 101-116

Chapter 7
On the Controllability for Neutral Stochastic Functional Differential Equations Driven by a Fractional Brownian motion in a Hilbert Space
(El Hassan Lakhe, National School of Applied Sciences, Cadi Ayyad University, Safi, Morocco)
pp. 117-130

Chapter 8
Controllability of Impulsive Neutral Stochastic Functional Integro-Differential Equations Driven by Fractional Brownian Motion
(El Hassan Lakhel and Mark A. McKibben, National School of Applied Sciences, Cadi Ayyad University, Safi, Morocco, and others)
pp. 131-148

Chapter 9
Specific Features of Brownian Diffusion of Nanoparticles in Micro-Nanodroplets
(Sergey P. Fisenko and Yuliya A. Khodyko, A.V. Luikov Heat and Mass Transfer, Institute of National Academy of Sciences of Belarus, Minsk, Belarus)
pp. 149-164

Chapter 10
Brownian Motion and the Formation of Dark Matter Haloes
(N. Hiotelis, 1st Lyceum of Athens, Ipitou, Plaka, Athens, Greece)
pp. 165-200

Chapter 11
Literature as a Diffusion Process
(Agamirza E. Bashirov and Gunash Bashirova, Eastern Mediterranean University, Gazimagusa, Turkey, and others)
pp. 201-218

Chapter 12
Almost Periodic Solution of some Stochastic Difference Equations
(Mamadou Moustapha Mbaye, Universite Gaston Berger de Saint-Louis, B.P., Saint-Louis, Senegal)
pp. 219-230

Chapter 13
Impulsive Stochastic Differential Equations Driven by G-Brownian Motion
(Lanying Hu, Yong Ren, Department of Mathematics, Anhui Normal University, Wuhu, China)
pp. 231-242

Chapter 14
Fractional Stochastic Differential Equations
(P. Balasubramaniam and P. Tamilalagan, Gandhigram Rural Institute-Deemed University, Tamil Nadu, India)
pp. 243-266

Chapter 15
Abstract Second-order Damped Stochastic Evolution Equations in a Hilbert Space Driven by Fractional Brownian Motion
(Mark A. McKibben and Micah Webster, West Chester University, Pennsylvania, and others)
pp. 267-288

Index
pp. 289-291

Audience: Professional researchers or graduate students in the areas of stochastic analysis, mathematical physics, differential equations.

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