Download or read book Generalized Diffusion Processes written by Nikola_ Ivanovich Portenko and published by American Mathematical Soc.. This book was released on 1990-12-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for diffusion in a medium moving in a nonregular way. The author constructs generalized diffusion processes under two assumptions: first, that the diffusion matrix is sufficiently regular; and second, that the drift vector is a function integrable to some power, or is a generalized function of the type of the derivative of a measure.

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Download or read book Analysis For Diffusion Processes On Riemannian Manifolds written by Feng-yu Wang and published by World Scientific. This book was released on 2013-09-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Download or read book Generalized Diffusion Processes written by Nikolaĭ Ivanovich Portenko and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for di.

Download or read book Schr dinger Equations and Diffusion Theory written by M. Nagasawa and published by Birkhäuser. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schrödinger Equations and Diffusion Theory addresses the question "What is the Schrödinger equation?" in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.

Download or read book Controlled Diffusion Processes written by N. V. Krylov and published by Springer Science & Business Media. This book was released on 2008-09-26 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.

Download or read book Elements of Random Walk and Diffusion Processes written by Oliver C. Ibe and published by John Wiley & Sons. This book was released on 2013-08-29 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.

Download or read book Diffusive Spreading in Nature Technology and Society written by Armin Bunde and published by Springer Nature. This book was released on 2023-05-08 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: What do the movements of molecules and the migration of humans have in common? How does the functionality of our brain tissue resemble the flow of traffic in New York City? How can understanding the spread of ideas, rumors, and languages help us tackle the spread a pandemic? This book provides an illuminating look into these seemingly disparate topics by exploring and expertly communicating the fundamental laws that govern the spreading and diffusion of objects. A collection of leading scientists in disciplines as diverse as epidemiology, linguistics, mathematics, and physics discuss various spreading phenomena relevant to their own fields, revealing astonishing similarities and correlations between the objects of study—be they people, particles, or pandemics. This updated and expanded second edition of an award-winning book introduces timely coverage of a subject with the greatest societal impact in recent memory—the global fight against COVID-19. Winner of the 2019 Literature Prize of the German Chemical Industry Fund and brainchild of the international and long-running Diffusion Fundamentals conference series, this book targets an interdisciplinary readership, featuring an introductory chapter that sets the stage for the topics discussed throughout. Each chapter provides ample opportunity to whet the appetite of those readers seeking a more in-depth treatment, making the book also useful as supplementary reading in appropriate courses dealing with complex systems, mass transfer, and network theory.

Download or read book Processes with Long Range Correlations written by Govindan Rangarajan and published by Springer. This book was released on 2008-01-11 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processes with long range correlations occur in a wide variety of fields ranging from physics and biology to economics and finance. This book, suitable for both graduate students and specialists, brings the reader up to date on this rapidly developing field. A distinguished group of experts have been brought together to provide a comprehensive and well-balanced account of basic notions and recent developments. The book is divided into two parts. The first part deals with theoretical developments in the area. The second part comprises chapters dealing primarily with three major areas of application: anomalous diffusion, economics and finance, and biology (especially neuroscience).

Download or read book Positive Harmonic Functions and Diffusion written by Ross G. Pinsky and published by Cambridge University Press. This book was released on 1995-01-12 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.

Download or read book Fluctuations Instabilities and Phase Transitions written by T. Riste and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the papers presented at the NATO Advanced Study Institute held at Geilo, Norway, 11th - 20th April 1975. The institute was the third in a row devoted to phase transitions. The previous two dealt with 2nd- and 1st-order transitions in equilibrium systems and the proceedings have been published.i~ In order to make an overlap wi th those institutes, the first part of this institute was devoted to 1st -or der transitions with an emphasis on the problems of metast abi l i t y and instability en countered i n spinodal decomposition, nucleation etc. The main topic was, however, that of non-equilibrium systems, and the present institute was to our knowledge the first one devoted to the physics of such systems. The discovery of the analogy between phase transitions in equilibrium systems and instabilities in non-equilibrium systems was first made by Rolf Landauer in 1961 and later independently by others. The analogy was first pointed out for electronic devices (tunnel diodes, Gunn oscillators, lasers, etc. ) and the treatment of hydrodynamic instabilities followed later.

Download or read book Methods of Mathematical Modelling written by Harendra Singh and published by CRC Press. This book was released on 2019-09-17 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications

Download or read book In Memoriam Marc Yor S minaire de Probabilit s XLVII written by Catherine Donati-Martin and published by Springer. This book was released on 2015-09-07 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents. With contributions by P. Salminen, J-Y. Yen & M. Yor; J. Warren; T. Funaki; J. Pitman& W. Tang; J-F. Le Gall; L. Alili, P. Graczyk & T. Zak; K. Yano & Y. Yano; D. Bakry & O. Zribi; A. Aksamit, T. Choulli & M. Jeanblanc; J. Pitman; J. Obloj, P. Spoida & N. Touzi; P. Biane; J. Najnudel; P. Fitzsimmons, Y. Le Jan & J. Rosen; L.C.G. Rogers & M. Duembgen; E. Azmoodeh, G. Peccati & G. Poly, timP-L Méliot, A. Nikeghbali; P. Baldi; N. Demni, A. Rouault & M. Zani; N. O'Connell; N. Ikeda & H. Matsumoto; A. Comtet & Y. Tourigny; P. Bougerol; L. Chaumont; L. Devroye & G. Letac; D. Stroock and M. Emery.

Download or read book Functional Analysis in Markov Processes written by M. Fukushima and published by Springer. This book was released on 2006-11-14 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Random Walk and Diffusion Models written by Wolf Schwarz and published by Springer Nature. This book was released on 2022-10-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an accessible introduction to random walk and diffusion models at a level consistent with the typical background of students in the life sciences. In recent decades these models have become widely used in areas far beyond their traditional origins in physics, for example, in studies of animal behavior, ecology, sociology, sports science, population genetics, public health applications, and human decision making. Developing the main formal concepts, the book provides detailed and intuitive step-by-step explanations, and moves smoothly from simple to more complex models. Finally, in the last chapter, some successful and original applications of random walk and diffusion models in the life and behavioral sciences are illustrated in detail. The treatment of basic techniques and models is consolidated and extended throughout by a set of carefully chosen exercises.

Download or read book Stochastic Analysis and Partial Differential Equations written by Gui-Qiang Chen and published by American Mathematical Soc.. This book was released on 2007 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original research papers and expository articles from the scientific program of the 2004-05 Emphasis Year on Stochastic Analysis and Partial Differential Equations at Northwestern University. Many well-known mathematicians attended the events and submitted their contributions for this volume. Topics from stochastic analysis discussed in this volume include stochastic analysis of turbulence, Markov processes, microscopic lattice dynamics, microscopic interacting particle systems, and stochastic analysis on manifolds. Topics from partial differential equations include kinetic equations, hyperbolic conservation laws, Navier-Stokes equations, and Hamilton-Jacobi equations. A variety of methods, such as numerical analysis, homogenization, measure-theoretical analysis, entropy analysis, weak convergence analysis, Fourier analysis, and Ito's calculus, are further developed and applied. All these topics are naturally interrelated and represent a cross-section of the most significant recent advances and current trends and directions in stochastic analysis and partial differential equations. This volume is suitable for researchers and graduate students interested in stochastic analysis, partial differential equations, and related analysis and applications.