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Stochastic Calculus via Regularizations

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Stochastic Calculus via Regularizations/ by Francesco Russo, Pierre Vallois.
作者:	Russo, Francesco.
其他作者:	Vallois, Pierre.
面頁冊數:	XXXI, 638 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Analysis. -
電子資源:	https://doi.org/10.1007/978-3-031-09446-0
ISBN:	9783031094460

Stochastic Calculus via Regularizations
Russo, Francesco.

Stochastic Calculus via Regularizations[electronic resource] /by Francesco Russo, Pierre Vallois. - 1st ed. 2022. - XXXI, 638 p.online resource. - Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics,112039-148X ;. - Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics,6.

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 Itô 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.

ISBN: 9783031094460

Standard No.: 10.1007/978-3-031-09446-0doiSubjects--Topical Terms:

669490
Analysis.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Stochastic Calculus via Regularizations
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