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X-WR-CALNAME:Institute of Mathematics and Informatics
X-ORIGINAL-URL:https://math.bas.bg
X-WR-CALDESC:Събития за Institute of Mathematics and Informatics
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DTSTART:20250330T010000
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DTSTART;TZID=Europe/Sofia:20251111T140000
DTEND;TZID=Europe/Sofia:20251111T153000
DTSTAMP:20260405T064431
CREATED:20251106T173729Z
LAST-MODIFIED:20251106T173729Z
UID:18448-1762869600-1762875000@math.bas.bg
SUMMARY:Семинар по приложна математика
DESCRIPTION:Следващата сбирка на Семинара по приложна математика ще бъде на 11.11. (вторник) от 14:00 в ИМИ-БАН\, Зала 503. \nДокладчик: Хелмут Питърс (Манхайм\, Германия) \nЗаглавие: The number of cycles in a random permutation and the number of segregating sites jointly converge to the Brownian sheet \nРезюме: 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. \n 
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d0%bf%d1%80%d0%b8%d0%bb%d0%be%d0%b6%d0%bd%d0%b0-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d0%ba%d0%b0-16/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
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BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20251015T150000
DTEND;TZID=Europe/Sofia:20251015T170000
DTSTAMP:20260405T064431
CREATED:20251006T195108Z
LAST-MODIFIED:20251006T195108Z
UID:18312-1760540400-1760547600@math.bas.bg
SUMMARY:Семинар по приложна математика
DESCRIPTION:Следващата сбирка на Семинара по приложна математика ще се проведе на 15.10 (сряда) от 15:00 в зала 503 на ИМИ-БАН. \nДоклад на тема \nStochastic scattering control of Walsh’s spider diffusion with optimal diffraction probability measure selected from its own local-time\nще изнесе Исаак Охави\, който работи в обалсти като стохастичен контрол\, стохастична оптимизация и частни диференциални уравнения. \nAbstract: 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. \nThe 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. \nReferences:  \n–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. \n-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\nno 22\, 2025.\n-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. \n-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
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d0%bf%d1%80%d0%b8%d0%bb%d0%be%d0%b6%d0%bd%d0%b0-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d0%ba%d0%b0-15/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
END:VEVENT
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