Stochastic calculus via regularizations / Francesco Russo, Pierre Vallois.
2022
QA274.2
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Title
Stochastic calculus via regularizations / Francesco Russo, Pierre Vallois.
Author
Russo, Francesco, 1959-
ISBN
9783031094460 (electronic bk.)
3031094468 (electronic bk.)
303109445X
9783031094453
3031094468 (electronic bk.)
303109445X
9783031094453
Publication Details
Cham, Switzerland : Springer, 2022.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-031-09446-0 doi
Call Number
QA274.2
Dewey Decimal Classification
519.2/2
Summary
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 Ito 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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed November 29, 2022).
Added Author
Vallois, Pierre.
Series
Bocconi & Springer series ; 11.
Available in Other Form
Print version: 9783031094453
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