Wydarzenia

W dniach 21-25 maja 2013 gościem Instytutu Matematycznego UWr będzie prof. Wojbor A. Woyczyński (Case Weste Reserve University, USA). Wygłosi on cykl pięciu wykładów pt. Diffusive processes and stochastic differential equations. Wykłady będą odbywać się w godzinach 16:15-18:00 według następującego planu: 21.05 (wtorek), sala B, 22.05 (środa), sala 602, 23.05 (czwartek), sala WS 24.05 (piątek), sala 602, 25.05 (sobota), sala 602 Streszczenie 1. Random walk and its parabolic scaling limits, infinitesimal generator of Brownian motion. 2. Brownian motion as a measure on the space of continuous functions, nondifferentiability of smaple paths. 3. Poisson processes and their mixtures, transition to Levy processes. 4. Levy-Khinchine formula and infinitesimal generators of Levy processes. 5. Selfsimilar case and singular integrals, basic estimations. 6. Stochastic integrals with respect to Levy processes. 7. Ito sdes for Brownian and other Levy processes and the corresponding linear pdes. 8. Interacting particle systems and their scaling limits. 9. Asymmetric exclusion processes and nonlinear conservation laws. 10. Propagation of chaos for Burgers equations, nonlinear McKean processes, and their nonlocal versions.

W dniach 7-16 maja 2013r. gościem Instytutu Matematycznego Uniwersytetu Wrocławskiego będzie prof. Eugene Lytvynov (Swansea University, UK). Wygłosi on cykl wykładów w ramach Środowiskowych Studiów Doktoranckich Nauk Matematycznych pt. Orthogonal decompositions for generalized stochastic processes with independent values. Plan wykładów wtorek 7.05.2013, godz. 12.00-14.00, sala WS czwartek 9.05.2013, godz. 10.00-12.00, sala 603 oraz godz. 14.00-16.00, sala 605 czwartek 16.05.2013, godz. 10.00-12.00, sala 603 oraz godz. 14.00-16.00, sala 605. Streszczenie: A generalized stochastic process is a probability measure on a space of generalized functions on the Euclidean space, that is, a random generalized function. One says that a generalized stochastic processes has independent values if the value of this function at a given point is independent of the values of the function at other points. (The latter is, of course, only a heuristic definition as one can not rigorously speak of a value of a generalized function at a given point.) A generalized stochastic processes with independent values over the real line can also be treated as the derivative of a classical stochastic processes with independent value (in particular, a Levy process). Our aim is the study of the space of square integrable functionals of a generalized stochastic processes with independent values. We will show that there is a natural unitary operator between a certain symmetric Fock space and the L^2-space. This extends the well known results related to the Wiener-Ito-Segal isomorphism for the Gaussian measure and a similar orthogonal decomposition in multiple stochastic integrals for the Poisson measure. We will also study other natural realizations of the L^2-space in terms of Fock-type spaces, in particular, the Nualart-Schoutens decomposition. In our research, we will heavily use not only probability theory, but also functional analysis, in particular, the theory of unbounded self-adjoint operators.