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Author : H. Jerome Keisler
Publisher :
ISBN 13 : 9781470407070
Total Pages : 184 pages
Book Rating : 4.4/5 (7 download)
Download or read book An Infinitesimal Approach to Stochastic Analysis written by H. Jerome Keisler and published by . This book was released on 1984 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. Jerome Keisler
Publisher :
ISBN 13 : 9780608075587
Total Pages : 195 pages
Book Rating : 4.0/5 (755 download)
Download or read book An Infinitesimal Approach to Stochastic Analysis written by H. Jerome Keisler and published by . This book was released on 1984 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. Jerome Keisler
Publisher : American Mathematical Soc.
ISBN 13 : 0821822977
Total Pages : 197 pages
Book Rating : 4.8/5 (218 download)
Download or read book An Infinitesimal Approach to Stochastic Analysis written by H. Jerome Keisler and published by American Mathematical Soc.. This book was released on 1984 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph uses Robinson's infinitesimal (i.e., nonstandard) analysis to study stochastic integral equations with respect to a Brownian motion. By using a combination of standard and infinitesimal methods, we obtain new results about stochastic integral equations which can be stated in standard terms.
Author :
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (928 download)
Download or read book An infinitesimal approach to stochastic analysis written by and published by . This book was released on 1991 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K.D. Stroyan
Publisher : Elsevier
ISBN 13 : 0080960421
Total Pages : 491 pages
Book Rating : 4.0/5 (89 download)
Download or read book Foundations of Infinitesimal Stochastic Analysis written by K.D. Stroyan and published by Elsevier. This book was released on 2011-08-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Author : Frederik S. Herzberg
Publisher : Springer
ISBN 13 : 3642331491
Total Pages : 125 pages
Book Rating : 4.6/5 (423 download)
Download or read book Stochastic Calculus with Infinitesimals written by Frederik S. Herzberg and published by Springer. This book was released on 2012-11-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Author : Josef Berger
Publisher :
ISBN 13 :
Total Pages : 83 pages
Book Rating : 4.:/5 (634 download)
Download or read book An Infinitesimal Approach to Stochastic Analysis on Abstract Wiener Spaces written by Josef Berger and published by . This book was released on 2002 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frederik S. Herzberg
Publisher : Springer
ISBN 13 : 9783642331503
Total Pages : 112 pages
Book Rating : 4.3/5 (315 download)
Download or read book Stochastic Calculus with Infinitesimals written by Frederik S. Herzberg and published by Springer. This book was released on 2012-11-07 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Author : H. Jerome Keisler
Publisher :
ISBN 13 :
Total Pages : 968 pages
Book Rating : 4.F/5 ( download)
Download or read book Elementary Calculus written by H. Jerome Keisler and published by . This book was released on 1976 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joseph L. McCauley
Publisher : Cambridge University Press
ISBN 13 : 0521763401
Total Pages : 219 pages
Book Rating : 4.5/5 (217 download)
Download or read book Stochastic Calculus and Differential Equations for Physics and Finance written by Joseph L. McCauley and published by Cambridge University Press. This book was released on 2013-02-21 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.
Author : K. D. Stroyan
Publisher :
ISBN 13 : 9780044879275
Total Pages : 478 pages
Book Rating : 4.8/5 (792 download)
Download or read book Foundations of Infinitesimal Stochastic Analysis written by K. D. Stroyan and published by . This book was released on 1986 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Author : Hiroyuki Matsumoto
Publisher : Cambridge University Press
ISBN 13 : 1108107885
Total Pages : 359 pages
Book Rating : 4.1/5 (81 download)
Download or read book Stochastic Analysis written by Hiroyuki Matsumoto and published by Cambridge University Press. This book was released on 2016-11-07 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.
Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 1316510085
Total Pages : 327 pages
Book Rating : 4.3/5 (165 download)
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author : Shigeo Kusuoka
Publisher : Springer Nature
ISBN 13 : 9811588643
Total Pages : 218 pages
Book Rating : 4.8/5 (115 download)
Download or read book Stochastic Analysis written by Shigeo Kusuoka and published by Springer Nature. This book was released on 2020-10-20 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas. In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations.
Author : D. Kannan
Publisher : CRC Press
ISBN 13 : 1482294702
Total Pages : 808 pages
Book Rating : 4.4/5 (822 download)
Download or read book Handbook of Stochastic Analysis and Applications written by D. Kannan and published by CRC Press. This book was released on 2001-10-23 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)
Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Zhi-yuan Huang
Publisher : Springer Science & Business Media
ISBN 13 : 9401141088
Total Pages : 308 pages
Book Rating : 4.4/5 (11 download)
Download or read book Introduction to Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).
