Wydarzenia

26 paździe ika w godzinach 16:15-18:00 w sali 602,w ramach Seminarium z Analitycznych i Funkcjonalnych Metod Teorii Prawdopodobieństwa, odbędzie się wykład dr. Rafała Łochowskiego z Katedra Ekonomii Matematycznej SGH pt. On Truncated Variation of Brownian Motion with Drift.. Streszczenie: In the paper *On Truncated Variation of Brownian Motion with Drift* (Bull. Pol. Acad. Sci. Math. 56 (2008), 267--281) we defined truncated variation of Brownian motion with drift. For positive $c$ we define two related quantities - upward and downward truncated variation. We prove that exponential moments of the above quantities are finite (in opposite to the regular variation, corresponding to Truncated Variation, which is infinite almost surely). We present estimates of the expected value of Upward Truncated Variation up to universal constants. As an application we give some estimates of the maximal possible gain from trading a financial asset in the presence of flat commission (proportional to the value of the transaction) when the dynamics of the prices of the asset follows a geometric Browniam motion process. In the presented estimates upward truncated variation appears naturally.

12 paździe ika w godzinach 16:15-18:00 w sali 601,w ramach Seminarium z Analitycznych i Funkcjonalnych Metod Teorii Prawdopodobieństwa, odbędzie się wykład prof. Stefana Schwabika z Czeskiej Akademii Nauk pt. General integration, extensions and applications to the Henstock-Kurzweil integral. Streszczenie: A general integration will be described in the flavour of the well-known book of Stanislaw Saks. An order in the structure of general integrals will be introduced. The concept of extending integrals will be presented, together with the classical and known Cauchy and Ha ack extensions, new extensions will be given and applied to the Lebesgue integral for obtaining characterizations of the Henstock-Kurzweil integral which is known to be equivalent to the narrow Denjoy or Perron integral.

28 września w godzinach 10:15-12:00 w sali WS odbędzie się wykład prof. Thomasa Mikoscha pt. Multivariate regular variation. Streszczenie: The notion of multivariate regular varition (mvr) arises as domain of attraction condition for partial sums of iid random vectors, maxima of iid random variables and in the context of stochastic recurrence equation. In a way, mvr is a natural extension to higher dimensions of power law behavior in the tails of distributions. In the first part of the talk we discuss under which circumstances regular variation of all linear combinations of a random vector implies mvr of the vector. In a second part we discuss under which circumstances the regular variation of a functional of some independent random variables or stochastic processes (such as products of independent variables, stochastic integrals or a linear combination with fixed coefficients) implies regular variation of the underlying independent components. In a third part we discuss extensions of mvr to function spaces and consequences for heavy-tailed large deviation results for partial sum processes of Donsker type.