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Author: Daniel W. Stroock Publisher: Cambridge University Press ISBN: 0521333660 Category : Mathematics Languages : en Pages : 141
Book Description
This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.
Author: Daniel W. Stroock Publisher: Cambridge University Press ISBN: 0521333660 Category : Mathematics Languages : en Pages : 141
Book Description
This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.
Author: Kiyosi Ito Publisher: Springer Science & Business Media ISBN: 3662100657 Category : Mathematics Languages : en Pages : 246
Book Description
This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.
Author: David F. Anderson Publisher: Springer ISBN: 3319168959 Category : Mathematics Languages : en Pages : 91
Book Description
This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other areas of science and technology. These notes are based in part on lectures given by Professor Anderson at the University of Wisconsin – Madison and by Professor Kurtz at Goethe University Frankfurt.
Author: Giuseppe Da Prato Publisher: Springer ISBN: 8876424997 Category : Mathematics Languages : en Pages : 286
Book Description
This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made.
Author: Valery I. Klyatskin Publisher: Elsevier ISBN: 008050485X Category : Science Languages : en Pages : 211
Book Description
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''oil slicks''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data.This raises a host of challenging mathematical issues. One could rarely solve such systems exactly (or approximately) in a closed analytic form, and their solutions depend in a complicated implicit manner on the initial-boundary data, forcing and system's (media) parameters . In mathematical terms such solution becomes a complicated "nonlinear functional" of random fields and processes.Part I gives mathematical formulation for the basic physical models of transport, diffusion, propagation and develops some analytic tools.Part II sets up and applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. The exposition is motivated and demonstrated with numerous examples.Part III takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering).Each chapter is appended with problems the reader to solve by himself (herself), which will be a good training for independent investigations.·This book is translation from Russian and is completed with new principal results of recent research.·The book develops mathematical tools of stochastic analysis, and applies them to a wide range of physical models of particles, fluids, and waves.·Accessible to a broad audience with general background in mathematical physics, but no special expertise in stochastic analysis, wave propagation or turbulence
Author: Nicolas Privault Publisher: Springer ISBN: 3642023800 Category : Mathematics Languages : en Pages : 322
Book Description
This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.
Author: Fima C. Klebaner Publisher: Imperial College Press ISBN: 1860945554 Category : Mathematics Languages : en Pages : 431
Book Description
This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
Author: Sergio Fajardo Publisher: Cambridge University Press ISBN: 1108619266 Category : Mathematics Languages : en Pages : 150
Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourteenth publication in the Lecture Notes in Logic series, Fajardo and Keisler present new research combining probability theory and mathematical logic. It is a general study of stochastic processes using ideas from model theory, a key central theme being the question, 'When are two stochastic processes alike?' The authors assume some background in nonstandard analysis, but prior knowledge of model theory and advanced logic is not necessary. This volume will appeal to mathematicians willing to explore new developments with an open mind.
Author: Jim Pitman Publisher: Springer Science & Business Media ISBN: 354030990X Category : Mathematics Languages : en Pages : 257
Book Description
The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Author: Daniel W. Stroock
Author: Daniel W. Stroock
Author: Kiyosi Ito
Author: Anatolij V. Skorochod
Author: David F. Anderson
Author: Giuseppe Da Prato
Author: Valery I. Klyatskin
Author: Nicolas Privault
Author: Fima C. Klebaner
Author: Sergio Fajardo
Author: Jim Pitman