An Infinitesimal Approach to Stochastic Analysis
Title | An Infinitesimal Approach to Stochastic Analysis PDF eBook |
Author | H. Jerome Keisler |
Publisher | |
Total Pages | 184 |
Release | 1984 |
Genre | Brownian motion processes |
ISBN | 9781470407070 |
An Infinitesimal Approach to Stochastic Analysis
Title | An Infinitesimal Approach to Stochastic Analysis PDF eBook |
Author | H. Jerome Keisler |
Publisher | |
Total Pages | 195 |
Release | 1984 |
Genre | |
ISBN | 9780608075587 |
Foundations of Infinitesimal Stochastic Analysis
Title | Foundations of Infinitesimal Stochastic Analysis PDF eBook |
Author | K.D. Stroyan |
Publisher | Elsevier |
Total Pages | 491 |
Release | 2011-08-18 |
Genre | Computers |
ISBN | 0080960421 |
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.
An Infinitesimal Approach to Stochastic Analysis
Title | An Infinitesimal Approach to Stochastic Analysis PDF eBook |
Author | H. Jerome Keisler |
Publisher | American Mathematical Soc. |
Total Pages | 197 |
Release | 1984 |
Genre | Brownian motion processes |
ISBN | 0821822977 |
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.
Stochastic Calculus with Infinitesimals
Title | Stochastic Calculus with Infinitesimals PDF eBook |
Author | Frederik S. Herzberg |
Publisher | Springer |
Total Pages | 125 |
Release | 2012-11-06 |
Genre | Mathematics |
ISBN | 3642331491 |
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.
Stochastic Calculus with Infinitesimals
Title | Stochastic Calculus with Infinitesimals PDF eBook |
Author | Frederik S. Herzberg |
Publisher | Springer |
Total Pages | 112 |
Release | 2012-11-07 |
Genre | Mathematics |
ISBN | 9783642331503 |
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.
Elementary Calculus
Title | Elementary Calculus PDF eBook |
Author | H. Jerome Keisler |
Publisher | |
Total Pages | 968 |
Release | 1976 |
Genre | Mathematics |
ISBN |