Malliavin calculus

Head of the seminar: Prof. A.A.Dorogovtsev

17.00, room 208.

Secretary of the seminar: G.Ryabov

Recordings of past seminars.

  • Seminar, September 27

    Speaker: Oleg Zaboronski (University of Warwick)

    Title: Probabilistic methods for the asymptotic analysis of Fredholm Determinants and Pfaffians

    Abstract: I will review the probabilistic method for computing large gap asymptotics of certain Fredholm determinants due to Marc Kac. The main idea is to interpret the corresponding trace-log expansion in terms of a random walk. I will then state some generalization of Kac’ theorem to the case of Fredholm Pfaffians both in the translation-invariant and non-invariant (Hankel) case. Finally, I will discuss application examples: the distribution of zeros for Kac polynomials, the distribution of eigenvalues for the real Ginibre ensemble of random matrices, gap probabilities and exit measures for systems of annihilating-coalescing Brownian motions.

  • Seminar, September 20

    Speaker: Mykola Portenko (Institute of Mathematics, NAS of Ukraine)

    Topic: Several comments to the behavior of Brownian motion in a Euclidean space with a membrane located on a given hyperplane.
    Abstract. My talk will concern the limit theorem for the number of crossings through the membrane by a discrete approximations of the process indicated in  the title. I am going to discuss various ways for characterizing the limit  distribution in that theorem.

  • Seminar, September 13

    Speaker: Alexey Rudenko (Institute of Mathematics, NAS of Ukraine)

    Topic: An estimate for Hausdorff measure of the set of the intersections of several independent Brownian motions on Carnot group

  • Seminar, May 31

    Speaker: Naoufel Salhi (University of Carthage)

    Topic: Self-intersection local times as generalized functionals

  • Seminar, May 24

    Speaker: Mariia Belozerowa (Odessa Mechnikov National University)

    Topic: Lyapunov exponents and asymptotic behavior of solutions to stochastic differential equations with interaction

  • Seminar, May 17

    Speakers: Andrey Dorogovtsev (Institute of Mathematics, NAS of Ukraine), Jasmina Djordjevich (University of Oslo)

    Topic: Monge-Kantorovich problem for stochastic flows

  • Seminar, April 26

    Speaker: Ekaterina Glinyanaya (Institute of Mathematics, NAS of Ukraine)

    Topic: Orthogonalization of multiple integrals with respect to the point measure corresponding to the Arratia flow

  • Seminar, April 19th

    Speaker: Viktor Yuskovych (National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)

    Topic: On a limit behavior of solutions to multidimensional SDEs

  • Seminar, March 1

    Speaker: Georgii Riabov

    Topic: Modifications of stochastic flows generated by consistent sequences of Feller transition probabilities

  • Seminar, February 22

    Speaker: Xia Chen (University of Tennessee, Knoxville)

    Title: Intermittency for hyperbolic Anderson models with time-independent Gaussian noise
    Abstract. Intuitively, inttermittency refers to a state of the system with random noise in which the high peak is rare but real. In mathematics, it can be described in terms of moment asymptotics of the system.

    Compared to the parabolic Anderson equation, the inttermittency for hyperbolic Anderson equation is much harder and less investigated due to absence of Feynman-Kac formula that links the parabolic Anderson equation to Brownian motions. In this talk, I will report some recent progress in this direction. In particular, I will show how the large deviation technique is combined with Malliavin calculus to achieve the precise moment asymptotics.

    The talk is based on a collaborating work joint with Balan, R. and Chen, L.