Stochastic Calculus with Infinitesimals (Lecture Notes in Mathematics, Band 2067) - Softcover

Herzberg, Frederik S.

 
9783642331480: Stochastic Calculus with Infinitesimals (Lecture Notes in Mathematics, Band 2067)
Softcover
ISBN 10: 3642331483 ISBN 13: 9783642331480
Verlag: Springer, 2012

Inhaltsangabe

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.

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Von der hinteren Coverseite

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.

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Verlag
Springer
Erscheinungsdatum
2012
Sprache
Englisch
ISBN 10 
3642331483
ISBN 13 
9783642331480
Einband
Taschenbuch
Anzahl der Seiten
132
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Deutschland

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Vorgestellte Ausgabe

ISBN 10:  3642331505 ISBN 13:  9783642331503
Verlag: Springer, 2012
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