EAN: 9783642331480

STOCHASTIC CALCULUS WITH INFINITESIMALS LECTU...

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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