<p>This monograph covers the theory of Dirichlet forms. It examines the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes and summarizes the model-theoretic genericity of hyperfinite stochastic processes theory.</p>

Hyperfinite Dirichlet Forms and Stochastic Processes (Lecture Notes of the Unione Matematica Italiana, Vol. 10)

Science & Math

Albeverio, Sergio

Herzberg, Frederik S.

Fan, Ruzong

Mathematics

Springer

<p>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.</p>

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

Business & Money

Economics

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