Stochastic Calculus via Regularizations
Francesco Russo · Pierre Vallois
ліс 2022 · Bocconi & Springer Series Кніга 11 · Springer Nature
Электронная кніга
638
Старонкі
reportАцэнкі і водгукі не спраўджаны Даведацца больш
Пра гэту электронную кнігу
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.
Звесткі пра аўтара
Francesco Russo studied at the EPFL Lausanne and he obtained his PhD on ''Markov random fields". Then he spent several postdocs in Bielefeld, Bonn and ENST Paris (now Telecom Paris). Since then he has been active in various subjects of stochastic analysis with some interests in applications to mathematical physics, mathematical finance and energy management. He has coorganized many conferences in stochastic analysis and in particular the so called "Ascona Conference" which has been quite influencial. He was coeditor of eight volumes of proceedings of that conference, published by Birkhäuser. He has had regular collaborations with many international institutions such as the University of Bielefeld, the EPFL Lausanne, the University of Campinas (Brazil), the Luiss University in Rome. He was professor at the university of Paris 13 for almost 15 years where he directed the probability and statistics research time and he contributed to the development of probability thereby and he spent two years in the research institution Inria Rocquencourt and in Ecole des Ponts ParisTech. Pierre Vallois started his research career at the Laboratoire de Probabilités in Paris VI. He then held a professorship at the University Henri Poincaré (now the University of Lorraine) and carried out his research at the Institut Elie Cartan de Lorraine, where he had several responsibilities. He was head of the probability and statistics team contributing significantly to its development organizing 6 probability meetings. He was in charge of the mathematics department in the Faculty of Science and Technology. He was director of the Charles Hermite Federation, which promotes multidisciplinary collaborations between mathematics, computer science and automation, organizing three forums with industrialists. Since 2018 he is professor emeritus. His research topics are various: Brownian motion, Lévy and diffusion processes, generalized stochastic calculus and Brownian penalization. Since 2005, he has turned to applications and probabilistic and statistical modeling: tumor growth, biological sequence analysis (DNA), health (allergy), gene networks and insurance.
Ацаніце гэту электронную кнігу
Падзяліцеся сваімі меркаваннямі.
Чытанне інфармацыb
Смартфоны і планшэты
Усталюйце праграму "Кнігі Google Play" для Android і iPad/iPhone. Яна аўтаматычна сінхранізуецца з вашым уліковым запісам і дазваляе чытаць у інтэрнэце або па-за сеткай, дзе б вы ні былі.
Ноўтбукі і камп’ютары
У вэб-браўзеры камп’ютара можна слухаць аўдыякнігі, купленыя ў Google Play.
Электронныя кнiгi i iншыя прылады
Каб чытаць на такіх прыладах для электронных кніг, як, напрыклад, Kobo, трэба спампаваць файл і перанесці яго на сваю прыладу. Выканайце падрабязныя інструкцыі, прыведзеныя ў Даведачным цэнтры, каб перанесці файлы на прылады, якія падтрымліваюцца.
