Generalized Diffusion Processes

Author : Nikola_ Ivanovich Portenko
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 42,6 Mb
Release : 1990-12-21
Category : Mathematics
ISBN : 0821898264

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Generalized Diffusion Processes by Nikola_ Ivanovich Portenko Pdf

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.

Author : Nikolaĭ Ivanovich Portenko
Publisher : Unknown
Page : 128 pages
File Size : 40,5 Mb
Release : 1990
Category : Diffusion processes
ISBN : 1470444968

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Generalized Diffusion Processes by Nikolaĭ Ivanovich Portenko Pdf

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.

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 339 pages
File Size : 47,7 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

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.

Author : N. V. Krylov
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 53,9 Mb
Release : 2008-09-26
Category : Science
ISBN : 9783540709145

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Controlled Diffusion Processes by N. V. Krylov Pdf

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.

Author : Rúben Sousa,Manuel Guerra,Semyon Yakubovich
Publisher : Springer Nature
Page : 269 pages
File Size : 45,7 Mb
Release : 2022-07-27
Category : Mathematics
ISBN : 9783031052965

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Convolution-like Structures, Differential Operators and Diffusion Processes by Rúben Sousa,Manuel Guerra,Semyon Yakubovich Pdf

T​his book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.

Author : Ari Arapostathis,Vivek S. Borkar,Mrinal K. Ghosh
Publisher : Cambridge University Press
Page : 341 pages
File Size : 41,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780521768405

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Ergodic Control of Diffusion Processes by Ari Arapostathis,Vivek S. Borkar,Mrinal K. Ghosh Pdf

The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.

Author : M. Fukushima
Publisher : Springer
Page : 316 pages
File Size : 40,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391555

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Functional Analysis in Markov Processes by M. Fukushima Pdf

Author : Fudong Ge,YangQuan Chen,Chunhai Kou
Publisher : Springer
Page : 250 pages
File Size : 49,7 Mb
Release : 2018-01-08
Category : Technology & Engineering
ISBN : 9783319728964

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Regional Analysis of Time-Fractional Diffusion Processes by Fudong Ge,YangQuan Chen,Chunhai Kou Pdf

This monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distributed parameter systems and relevant basic control theory. New research problems are then defined in terms of their actuation and sensing policies within the regional analysis framework. The results presented provide insight into the control-theoretic analysis of fractional-order systems for use in real-life applications such as hard-disk drives, sleep stage identification and classification, and unmanned aerial vehicle control. The results can also be extended to complex fractional-order distributed-parameter systems and various open questions with potential for further investigation are discussed. For instance, the problem of fractional order distributed-parameter systems with mobile actuators/sensors, optimal parameter identification, optimal locations/trajectory of actuators/sensors and regional actuation/sensing configurations are of great interest. The book’s use of illustrations and consistent examples throughout helps readers to understand the significance of the proposed fractional models and methodologies and to enhance their comprehension. The applications treated in the book run the gamut from environmental science to national security. Academics and graduate students working with cyber-physical and distributed systems or interested in the applications of fractional calculus will find this book to be an instructive source of state-of-the-art results and inspiration for further research.

Author : Gui-Qiang Chen,Elton P. Hsu,Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 42,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840597

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Stochastic Analysis and Partial Differential Equations by Gui-Qiang Chen,Elton P. Hsu,Mark A. Pinsky Pdf

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.

Author : Sergio Albeverio,Philip Blanchard,L. Streit
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400921177

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Stochastic Processes and their Applications by Sergio Albeverio,Philip Blanchard,L. Streit Pdf

'Et moi ..., si j'avait su comment en revenIT, One service mathematics has rendered the je n'y serais point allt\.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. :; 'One service logic has rendered com puter science .. :; 'One service category theory has rendered mathematics .. :. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : Jean Jacod,Albert Shiryaev
Publisher : Springer Science & Business Media
Page : 682 pages
File Size : 46,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662052655

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Limit Theorems for Stochastic Processes by Jean Jacod,Albert Shiryaev Pdf

This volume by two international leaders in the field proposes a systematic exposition of convergence in law for stochastic processes from the point of view of semimartingale theory. It emphasizes results that are useful for mathematical theory and mathematical statistics. Coverage develops in detail useful parts of the general theory of stochastic processes, such as martingale problems and absolute continuity or contiguity results.

Author : Hiroshi Tanaka,Makoto Maejima,Tokuzo Shiga
Publisher : World Scientific
Page : 443 pages
File Size : 44,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9789810245917

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Stochastic Processes by Hiroshi Tanaka,Makoto Maejima,Tokuzo Shiga Pdf

A selection of Hiroshi Tanaka's brilliant works on stochastic processes and related topics.

Author : Wolf Schwarz
Publisher : Springer Nature
Page : 218 pages
File Size : 53,6 Mb
Release : 2022-10-06
Category : Mathematics
ISBN : 9783031121005

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Random Walk and Diffusion Models by Wolf Schwarz Pdf

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.

Author : Rainer Buckdahn,Hans J. Engelbert,Marc Yor
Publisher : CRC Press
Page : 296 pages
File Size : 49,8 Mb
Release : 2002-05-16
Category : Mathematics
ISBN : 9781482265231

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Stochastic Processes and Related Topics by Rainer Buckdahn,Hans J. Engelbert,Marc Yor Pdf

This volume comprises selected papers presented at the 12th Winter School on Stochastic Processes and their Applications, which was held in Siegmundsburg, Germany, in March 2000. The contents include Backward Stochastic Differential Equations; Semilinear PDE and SPDE; Arbitrage Theory; Credit Derivatives and Models for Correlated Defaults; Three In

Author : Ole E. Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 44,8 Mb
Release : 2001-03-30
Category : Mathematics
ISBN : 081764167X

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Lévy Processes by Ole E. Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick Pdf

A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.