Paths And Processes
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| Author | : Kiyosi Itô |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642620256 |
Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
| Author | : Mark S. Swanson |
| Publisher | : Courier Corporation |
| Total Pages | : 463 |
| Release | : 2014-02-19 |
| Genre | : Science |
| ISBN | : 0486782301 |
Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.
| Author | : Mark S. Swanson |
| Publisher | : Courier Corporation |
| Total Pages | : 463 |
| Release | : 2014-02-19 |
| Genre | : Science |
| ISBN | : 0486493067 |
Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.
| Author | : Peter K. Friz |
| Publisher | : Cambridge University Press |
| Total Pages | : 670 |
| Release | : 2010-02-04 |
| Genre | : Mathematics |
| ISBN | : 9780521876070 |
Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.
| Author | : Horacio S. Wio |
| Publisher | : World Scientific |
| Total Pages | : 174 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 9814449040 |
This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920''s, corresponding to a sum over random trajectories, anticipating by two decades Feynman''s famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950''s. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.
| Author | : Mohamed Abdelghani |
| Publisher | : CRC Press |
| Total Pages | : 493 |
| Release | : 2020-07-14 |
| Genre | : Business & Economics |
| ISBN | : 0429809247 |
It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc. Authors Mohamed Abdelghani completed his PhD in mathematical finance from the University of Alberta, Edmonton, Canada. He is currently working as a vice president in quantitative finance and machine learning at Morgan Stanley, New York, USA. Alexander Melnikov is a professor in mathematical finance at the University of Alberta. His research interests belong to the area of contemporary stochastic analysis and its numerous applications in mathematical finance, statistics and actuarial science. He has written six books as well as over 100 research papers in leading academic journals.
| Author | : Horacio Sergio Wio |
| Publisher | : World Scientific |
| Total Pages | : 174 |
| Release | : 2013-01-18 |
| Genre | : Science |
| ISBN | : 9814449059 |
This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950's. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations. remove /a
| Author | : Peter K. Friz |
| Publisher | : Cambridge University Press |
| Total Pages | : 671 |
| Release | : 2010-02-04 |
| Genre | : Mathematics |
| ISBN | : 1139487213 |
Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.
| Author | : Jim Williams |
| Publisher | : John Wiley & Sons |
| Total Pages | : 322 |
| Release | : 2004-09-07 |
| Genre | : Business & Economics |
| ISBN | : 0787975346 |
Learning Paths is a down-to-earth practical resource that is filled with illustrative examples, methods, techniques, strategies, processes, and tools for making company-wide, real-time training possible. Created to be flexible, the Learning Path approach can be customized to fit your organization no matter what its type or size. Learning Paths is divided into three sections: The Learning Path Methodology: Walks the reader through the major steps and strategies needed for building Learning Paths. Doing the Right Training: Offers a wide-range of strategies, methods and techniques that can be targeted to the training within a Learning Path and tied to an organization’s particular business needs. Do the Training Right: Shows how to ensure the training within a Learning Path is delivered in the most cost-effective manner and introduces methods for structuring training so that it transfers to the job easily and effectively.
| Author | : Robert T. Balmer |
| Publisher | : Academic Press |
| Total Pages | : 905 |
| Release | : 2011-01-03 |
| Genre | : Technology & Engineering |
| ISBN | : 0123850738 |
Modern Engineering Thermodynamics - Textbook with Tables Booklet offers a problem-solving approach to basic and applied engineering thermodynamics, with historical vignettes, critical thinking boxes and case studies throughout to help relate abstract concepts to actual engineering applications. It also contains applications to modern engineering issues. This textbook is designed for use in a standard two-semester engineering thermodynamics course sequence, with the goal of helping students develop engineering problem solving skills through the use of structured problem-solving techniques. The first half of the text contains material suitable for a basic Thermodynamics course taken by engineers from all majors. The second half of the text is suitable for an Applied Thermodynamics course in mechanical engineering programs. The Second Law of Thermodynamics is introduced through a basic entropy concept, providing students a more intuitive understanding of this key course topic. Property Values are discussed before the First Law of Thermodynamics to ensure students have a firm understanding of property data before using them. Over 200 worked examples and more than 1,300 end of chapter problems provide an extensive opportunity to practice solving problems. For greater instructor flexibility at exam time, thermodynamic tables are provided in a separate accompanying booklet. University students in mechanical, chemical, and general engineering taking a thermodynamics course will find this book extremely helpful. Provides the reader with clear presentations of the fundamental principles of basic and applied engineering thermodynamics. Helps students develop engineering problem solving skills through the use of structured problem-solving techniques. Introduces the Second Law of Thermodynamics through a basic entropy concept, providing students a more intuitive understanding of this key course topic. Covers Property Values before the First Law of Thermodynamics to ensure students have a firm understanding of property data before using them. Over 200 worked examples and more than 1,300 end of chapter problems offer students extensive opportunity to practice solving problems. Historical Vignettes, Critical Thinking boxes and Case Studies throughout the book help relate abstract concepts to actual engineering applications. For greater instructor flexibility at exam time, thermodynamic tables are provided in a separate accompanying booklet.
