### Malliavin calculus

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

17.00, room 208.

Secretary of the seminar: G.Ryabov

- 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.* - Seminar, February 15
Speaker:

**Mykola Portenko**(Institute of Mathematics, NAS of Ukraine)Topic:

**Brownian motion in a Euclidean space with a membrane located on a given hyperplane.**The presentation is based on the results of joint investigations with Prof. Bohdan Kopytko.

Abstract.

*Brownian motion in a Euclidean space with a membrane located on a given hyperplane and acting in a normal direction is constructed such that its so-called permeability coefficient can be given by an arbitrary Borel measurable function defined on that hyperplane and taking on its values from the interval [-1,+1]. In all the publications on the topic, that coefficient was supposed to be a continuous function. A certain limit theorem for the number of crossings through the membrane by a discrete approximation of the process constructed is proved. The limit distribution in that theorem can be curiously interpreted in the case of the membrane whose permeability coefficient coincides with the indicator of a measurable subset of the hyperplane.* - Seminar, February 8
Speaker:

**Andrey Dorogovtsev**(Institute of Mathematics, NAS of Ukraine)Topic:

**Isonormal processes associated with Brownian motion** - Seminar, December 28
Speaker:

**Mykola Vovchanskyi**(Institute of Mathematics, NAS of Ukraine)Topic:

**On the convergence of 1-point densities for Arratia flows** - Seminar, December 21
Speaker:

**Mikhail Neklyudov**Topic:

**Ergodicity for infinite particle systems with locally conserved quantities**