Семинар по приложна математика
2025-10-15 15:00 - 17:00 (Europe/Sofia) | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Следващата сбирка на Семинара по приложна математика ще се проведе на 15.10 (сряда) от 15:00 в зала 503 на ИМИ-БАН.
Доклад на тема
Stochastic scattering control of Walsh’s spider diffusion with optimal diffraction probability measure selected from its own local-time
ще изнесе Исаак Охави, който работи в обалсти като стохастичен контрол, стохастична оптимизация и частни диференциални уравнения.
Abstract: In this talk, we start by giving a short introduction on “classical” stochastic control theory and its connection with second order nonlinear PDE theory. Then, we present Walsh’s spider diffusions living on a star-shaped network, and explain how these processes are at the origin of new problems of stochastic scattering control. A main direction is to focus and understand precisely their behavior and local time at the vertex. Thereafter, we will give the main ideas, steps and mathematical directions that I have recently undertaken in order to finally be able to prove existence and weak uniqueness of a spider’s motion having a spinning measure depending on its own local time.
The stochastic control problem aims to understand how the spider particle is diffracted at the vertex. The key point is to use the new boundary condition at the junction point, called: nonlinear local-time Kirchhoff’s boundary condition and the recent advances I have obtained in the analysis of nonlinear partial differential equations in the viscosity framework.
References:
–Comparison principle for Walsh’s spider HJB equations with non linear local time Kirchhoff’s boundary transmission. Journal of Mathematical Analysis and Applications, 547 (2), 2025.
-Martingal problem for a Walsh’s spider diffusion with spinning measure selected from its own local time. Accepted January 2025. Electronic Journal of Probability, Volume 30, paper
no 22, 2025.
-Well posedness of linear parabolic partial differential equations posed on a star-shaped network with local time Kirchhoff’s boundary condition at the vertex. Journal of Mathematical Analysis and Applications, 537 (2), 2024.
-Stochastic scattering control of spider diffusion governed by an optimal probability diffraction measure selected from its own local time. Submitted 2025, Arxiv arXiv:2501.18057

Семинар по приложна математика
2025-11-11 14:00 - 15:30
Следващата сбирка на Семинара по приложна математика ще бъде на 11.11. (вторник) от 14:00 в ИМИ-БАН, Зала 503.
Докладчик: Хелмут Питърс (Манхайм, Германия)
Заглавие: The number of cycles in a random permutation and the number of segregating sites jointly converge to the Brownian sheet
Резюме: Consider a random permutation of {1, …, ⌊nᵗ²⌋} drawn according to the Ewens measure with parameter t₁, and let K(n, t) denote the number of its cycles, where t ≡ (t₁, t₂) ∈ [0, 1]². Next, consider a sample drawn from a large, neutral population of haploid individuals subject to mutation under the infinitely many sites model of Kimura, whose genealogy is governed by Kingman’s coalescent. Let S(n, t) count the number of segregating sites in a sample of size ⌊nᵗ²⌋ when mutations arrive at rate t₁/2. Our main result comprises two different couplings of the above models for all parameters n ≥ 2 and t ∈ [0, 1]², such that in both couplings one has weak convergence of processes as n → ∞ to a one-dimensional Brownian sheet. This generalizes and unifies a number of well-known results.
