Bocconi & Springer : Bocconi & Springer - Francesco Russo

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Bocconi & Springer

By: Francesco Russo, Pierre Vallois

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Paperback | 16 November 2022

At a Glance

Paperback
672 Pages

Dimensions(cm)
23.5 x 15.49 x 3.66

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$249.75

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The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure of the integrator process, they generalize the usual It´ and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness. It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.

Industry Reviews

"There is a comprehensive list of 344 references, papers and books, and an index. The book will be a valuable source of ideas, techniques, results and illustrations to anyone, researcher, university lecturer, PhD student, applied scientist, etc. dealing with stochastic calculus and its applications." (Jordan M. Stoyanov, zbMATH 1529.60003, 2024)

"Russo and Vallois's book is an excellent and up-to-date monograph on stochastic analysis, with the theory of integration via regularization at its core. ... The book is a monograph at the advanced research level and essentially could be useful for researchers in stochastic analysis. ... The book is strongly recommendable for Ph.D. students and researchers in stochastic analysis." (Josep Vives, Mathematical Reviews, Issue (5), March, 2024)

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