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X-WR-CALDESC:Събития за Institute of Mathematics and Informatics
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BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20260512T140000
DTEND;TZID=Europe/Sofia:20260512T153000
DTSTAMP:20260628T121628
CREATED:20260507T084754Z
LAST-MODIFIED:20260507T084754Z
UID:19210-1778594400-1778599800@math.bas.bg
SUMMARY:Национален семинар по стохастика
DESCRIPTION:Поредната сбирка на \nНационалния семинар по стохастика\nще се проведе на 12 май 2026 г. (вторник) от 14:00 часа в зала 503 на ИМИ – БАН. \nДоклад на тема \nRandom Flights and Anomalous Diffusion: A non-Markovian Take on Lorentz Processes\nще изнесе \nLorenzo Facciaroni (Sapienza University of Rome). \nAbstract: A Lorentz process is a model for the motion of a particle among randomly located scatterers\, also known as obstacles. It was originally used to describe the transport of electrons through a conductor. In the classical setting\, when the scatterers are distributed according to a Poisson point process\, the deterministic dynamics of elastic collisions can be approximated\, under the Boltzmann-Grad scaling limit\, by a Markovian random flight. The density of this limiting process is governed by the Boltzmann equation. Passing further to the hydrodynamic limit\, one recovers Brownian motion as the macroscopic description of the particle’s position. In this work\, we introduce a new class of point processes that generalizes the Poisson process and we investigate the motion of a particle which collides elastically with obstacles distributed according to this distribution. Unlike the classical case\, the corresponding limiting random flight process is no longer Markovian. Instead\, it exhibits memory effects that lead to superdiffusive behavior. At the macroscopic level\, the particle’s position converges to a continuous superdiffusive process. Within this framework\, we derive a non-local analogue of the Boltzmann equation governing the non-Markovian random flight. Moreover\, we show that the density of the superdiffusive scaling limit satisfies a fractional heat equation\, reflecting the anomalous transport induced by the underlying correlations. \nKeywords: Lorentz process · Boltzmann-Grad limit · Feller semigroups. \nReferences:\n1. Facciaroni\, L.\, Ricciuti\, C.\, Scalas\, E.\, Toaldo\, B. (2026+) Random Flights and Anomalous Diffusion: A non Markovian Take on Lorentz Processes. To appear in Annals of Applied Probability.\n2. Gallavotti\, G. (1972) Rigorous Theory of the Boltzmann Equation in the Lorentz Gas. Nota interna n. 358\, Istituto di Fisica\, Università di Roma.\n3. Lorentz\, H.A. (1905) The motion of electrons in metallic bodies I. In: Proc. Acad. Amst.\, 7\, 438-453.\n4. Sphon\, H. (1978) The Lorentz process converges to a random flight. Commun. Math. Phys.\, 60\, 277-290. \nПовече информация за доклада можете да намерите на страницата на семинара:\nhttp://www.math.bas.bg/~statlab/NSPS/ \n 
URL:https://math.bas.bg/event/%d0%bd%d0%b0%d1%86%d0%b8%d0%be%d0%bd%d0%b0%d0%bb%d0%b5%d0%bd-%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d1%81%d1%82%d0%be%d1%85%d0%b0%d1%81%d1%82%d0%b8%d0%ba%d0%b0-47/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%98%D0%BD%D1%81%D1%82%D0%B8%D1%82%D1%83%D1%82%20%D0%BF%D0%BE%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20%D0%B8%20%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20-%20%D0%91%D0%90%D0%9D":MAILTO:office@math.bas.bg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20260513T140000
DTEND;TZID=Europe/Sofia:20260513T153000
DTSTAMP:20260628T121628
CREATED:20260507T085819Z
LAST-MODIFIED:20260507T085819Z
UID:19214-1778680800-1778686200@math.bas.bg
SUMMARY:Национален семинар по стохастика
DESCRIPTION:Поредната сбирка на \nНационалния семинар по стохастика\nще се проведе на 13 май 2026 г. (вторник) от 14:00 часа в зала 503 на ИМИ – БАН. \nДоклад на тема \nSome Properties of Exponential Functionals of Continuous Gaussian Processes\nще изнесе \nJosé Alfredo López-Mimbela (Center for Research in Mathematics Guanajuato\, Mexico). \nAbstract: Exponential functionals of random processes are mathematical expressions that typically involve integrating the exponential of a random process over time. These functionals play a significant role in various areas of mathematics and applied sciences\, including probability theory\, statistical mechanics\, and financial mathematics. In this talk\, we discuss some properties of exponential functionals associated with continuous Gaussian processes. The discussion centers on obtaining useful bounds for their cumulative distribution functions\, with particular emphasis on Brownian motion and fractional Brownian motion. \nПовече информация за доклада можете да намерите на страницата на семинара:\nhttp://www.math.bas.bg/~statlab/NSPS/ \n 
URL:https://math.bas.bg/event/%d0%bd%d0%b0%d1%86%d0%b8%d0%be%d0%bd%d0%b0%d0%bb%d0%b5%d0%bd-%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d1%81%d1%82%d0%be%d1%85%d0%b0%d1%81%d1%82%d0%b8%d0%ba%d0%b0-48/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%98%D0%BD%D1%81%D1%82%D0%B8%D1%82%D1%83%D1%82%20%D0%BF%D0%BE%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20%D0%B8%20%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20-%20%D0%91%D0%90%D0%9D":MAILTO:office@math.bas.bg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20260520T140000
DTEND;TZID=Europe/Sofia:20260520T153000
DTSTAMP:20260628T121628
CREATED:20260517T124507Z
LAST-MODIFIED:20260517T124507Z
UID:19289-1779285600-1779291000@math.bas.bg
SUMMARY:Национален семинар по стохастика
DESCRIPTION:Поредната сбирка на \nНационалния семинар по стохастика\nще се проведе на 20 май 2026 г. (вторник) от 14:00 часа в зала 503 на ИМИ – БАН. \nДоклад на тема \nFinite time blowup and existence of global solutions of a semi-linear stochastic partial differential equation with fractional noise\nще изнесе \nEkaterina Todorova Kolkovska (Center for Research in Mathematics Guanajuato\, Mexico). \nAbstract: We consider a stochastic partial differential equation driven by fractional Brownian motion with Hurst parameter H greater or equal to 1/2 on a bounded domain with smooth boundary and Dirichlet boundary conditions. By means of an associated random partial differential equation\, lower and upper bounds for the blowup time of the solution are given. Sufficient conditions for blowup in finite time and for the existence of a global solution are deduced in terms of the parameters of the equation. For the case H = 1/2 (i.e. for Brownian motion) estimates for the probability of blowup in finite time are given in terms of the laws of exponential functionals of Brownian motion. \nПовече информация за доклада можете да намерите на страницата на семинара:\nhttp://www.math.bas.bg/~statlab/NSPS/ \n 
URL:https://math.bas.bg/event/%d0%bd%d0%b0%d1%86%d0%b8%d0%be%d0%bd%d0%b0%d0%bb%d0%b5%d0%bd-%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d1%81%d1%82%d0%be%d1%85%d0%b0%d1%81%d1%82%d0%b8%d0%ba%d0%b0-49/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%98%D0%BD%D1%81%D1%82%D0%B8%D1%82%D1%83%D1%82%20%D0%BF%D0%BE%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20%D0%B8%20%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20-%20%D0%91%D0%90%D0%9D":MAILTO:office@math.bas.bg
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