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Stochastic Calculus with Infinitesimals (Paperback, 2013 ed.)
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Stochastic Calculus with Infinitesimals (Paperback, 2013 ed.)
Series: Lecture Notes in Mathematics, 2067
Expected to ship within 10 - 15 working days
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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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