sažeci za ak. god. 2026./2027.

Obrisani Korisnik — Tue, 13 Oct 2026 11:06:59 GMT

Parameter estimation of some threshold diffusions

Threshold diffusions are solutions to stochastic differential equations whose coefficients are discontinuous functions. They are used to model various phenomena in finance, economics, engineering, and other scientific fields. In this seminar, we will focus on parameter estimation problems, discussing asymptotic results under different assumptions and highlighting the technical challenges arising, in particular, from the interplay between discontinuities and local times.

When Collisions Remember: Para-Markov Dynamics and Kinetic Limits

How can memory survive a kinetic limit that eliminates recollisions? Starting from continuous-time random walks on general state spaces, this talk compares Markov, semi-Markov and para-Markov dynamics, highlighting how dependence between waiting times shapes their evolution equations. We then connect these ideas to Gallavotti’s approach to the Lorentz gas. Mittag–Leffler obstacle fields, introduced through their finite-dimensional distributions, generate dependent free flights whose memory persists in the Boltzmann–Grad limit. A subsequent mixing representation provides a bridge to models with random speed and fractional kinetic equations. Finally, we examine how these distinct microscopic mechanisms lead to the same diffusion limit, while revealing subtle differences between finite-speed superdiffusion, heavy tails and self-similarity.

Joint work with: L. Facciaroni, C. Ricciuti and E. Scalas

Bregman Divergence in PDEs and Probability

Bregman divergence, generated by a convex function, provides a natural counterpart of squared distance. I will discuss the corresponding Sobolev–Bregman forms associated with Markov semigroups and nonlocal operators, and their connections with energy identities in partial differential equations. The main focus will be on Bregman variation of semimartingales—a nonlinear analogue of quadratic variation that captures both continuous evolution and jumps. A Bregman version of Itô’s formula reveals links between convexity, stochastic processes, and nonlinear analytic forms.

Pattern Recovery by Convex Non-Differentiable Regularizers

Many modern statistical problems are high-dimensional, but the underlying signal often has much simpler structure than its ambient dimension suggests. Regularization is a natural way to exploit this structure: while the LASSO promotes sparsity, penalties such as the fused LASSO and SLOPE can recover richer patterns, including plateaus and clusters of coefficients with equal magnitude.

In this talk, I will present a geometric view of such patterns through subdifferentials and dual balls, and show how this geometry determines asymptotic pattern recovery. I will discuss when exact recovery is possible, why standard fused LASSO can fail, and how adaptive or weighted variants can repair this. I will also outline how these ideas extend to high-dimensional estimation beyond decomposable penalties, with illustrations from insurance data and graphical models.

seminari u ak. god. 2026./2027.

Obrisani Korisnik — Tue, 13 Oct 2026 11:08:39 GMT

20.10.2026.
- Bruno Toaldo (University of Turin) :: When Collisions Remember: Para-Markov Dynamics and Kinetic Limits
- Sara Mazzonetto (University of Lorraine) :: Parameter estimation of some threshold diffusions
6.10.2026.
- Małgorzata Bogdan (University of Wrocław) :: Pattern Recovery by Convex Non-Differentiable Regularizers
- Krzysztof Bogdan (Wrocław University of Science and Technology) :: Bregman Divergence in PDEs and Probability

ČLANOVI SEMINARA

Obrisani Korisnik — Tue, 06 Oct 2026 07:28:53 GMT

Bojan Basrak, Adrian Beker, Ivan Biočić, Dubravka Božić, Darko Brborović, Marina Dajaković, Petra Daković, Vesna Gotovac Đogaš, Danijel Grahovac, Diana Hunjak, Miljenko Huzak, Daniela Ivanković, Krunoslav Ivanović, Nina Kamčev, Danijel Krizmanić, Petra Lazić, Snježana Lubura Strunjak, Dominik Mihalčić, Rudi Mrazović, Ivan Papić, Hrvoje Planinić, Petra Posedel Šimović, Nikola Sandrić, Ivana Slamić, Siniša Slijepčević, Tatjana Slijepčević-Manger, Stjepan Šebek, Hrvoje Šikić, Luka Šimek, Kristina Ana Škreb, Antonio Špac, Nenad Šuvak, Tvrtko Tadić, Azra Tafro, Tadej Petar Tukara, Ivana Valentić, Zoran Vondraček, Milena Vulević Pribudić, Vanja Wagner, Petra Žugec

PMF - Seminar za teoriju vjerojatnosti

sažeci za ak. god. 2026./2027.

seminari u ak. god. 2026./2027.

ČLANOVI SEMINARA