Intensive course on "Chaos, Expansions and Itô Calculus"
Novi Sad, Serbia, Sept. 23 - 30, 2010.

DAAD—Project in the framework of the Stability Pact for South East Europe

Center of excellences for applications of mathematics

Intensive course

Chaos, Expansions and Itô Calculus

September 23 - 30, 2010

Faculty of Sciences, Novi Sad,

     Department of Mathematics and Informatics

 

Lecturers:

•   Stevan Pilipović, University of Novi Sad, Serbia

•   Dora Seleši, University of Novi Sad, Serbia

•  Tijana Levajković, University of Belgrade, Serbia

• Radoslava Mirkov, University of Berlin, Germany

Program: 6 lectures of 45 minutes per day, coffee break and lunch break

Themes:

·        Spaces of (deterministic) generalized functions; A characterization of tempered distributions by Hermite functions and Hermite polynomials

·        Nuclear spaces, inductive and projective limits of Hilbert spaces, Gelfand triples

·        White noise space; A construction of the Gaussian measure on infinite dimensional spaces

·        Fock spaces and second quantization operators; Eigenvalues and eigenvectors of the harmonic oscillator and its second quantization

·        The Wiener-Ito chaos expansion; A series representation of Brownian motion and white noise process

·        Spaces of stochastic generalized functions (Hida, Kondratiev and other weight spaces)

·        The Wick product

·        Generalized stochastic processes

·        Ito calculus; The classical Ito calculus with ordinary products versus Hida-Ito calculus with Wick products

·        Hilbert space valued generalized stochastic processes

·        The Malliavin derivative and the Skorokhod integral in chaos expansion representation

·        Stochastic differential equations via chaos expansion methods; The stochastic Dirichlet problem, the Helmholtz equation, equations involving the Ornstein-Uhlenbeck operator etc.

Contact/Application:

pilipovic@dmi.uns.ac.rs

dora@dmi.uns.ac.rs

Arrival and registration on September 23rd PM or September 24th AM.

Lectures start on September 24th at 10 AM.

Departure on September 29th PM or September 30th AM.

Accommodation will be provided at the students dormitory "Sajmiste", Slobodana Bajica 17.

(find it on the map) best reachable with bus line number 11.

Lectures will be held at the Department of Mathematics and Informatics, Trg Dositeja Obradovica 4.

(find it on the map) best reachable with bus line number 4, starting from the railway/bus station.