### Malliavin calculus

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

17.00, room 208.

Secretary of the seminar: G.Ryabov

- 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.*