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X-WR-CALNAME:Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences
X-ORIGINAL-URL:http://math.bas.bg/en/
X-WR-CALDESC:Events for Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences
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DTSTART:20180325T010000
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DTSTART:20181028T010000
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DTSTART;TZID="Europe/Sofia":20181017T140000
DTEND;TZID="Europe/Sofia":20181017T160000
DTSTAMP:20190921T140703
CREATED:20181011T122442Z
LAST-MODIFIED:20181018T211922Z
UID:6093-1539784800-1539792000@math.bas.bg
SUMMARY:National Seminar on Probability and Statistics
DESCRIPTION:The next meeting of \nthe National Seminar on Probability and Statistics\n \nwill be held on October 17\, 2018 (Wednesday) at 2 p.m. in Room 403 of IMI-BAS. A talk will be delivered by \nDoncho Donchev (FMI\, Sofia University) \non: \nAsymptotic Solutions of Shiryaev’s Inverse Problem\nAbtract: In our recent paper\, we characterized the exit density of a Brownian motion through one-sided smooth boundaries in terms of a solution of some parabolic second-order PDE. It turns out that this equation can be reduced to a first-order PDE. It is shown that the solution to the last equation admits an analytic representation only for three classes of boundaries – parabolic boundaries\, square-root boundaries and rational boundaries. Our approach is substantiated by an example\, where we find the exit density of a boundary not studied so far. \nNext\, we discuss the inverse first exit problem. We derive an asymptotic formula\, that describes the small time behaviour of the exit density p_f(t) that corresponds to a boundary f(t). Making use of this formula\, we construct a function f(t) such that log(p_f(t))=log(p_eta(t))+ o(t) for a large family of densities p_eta(t) of non-negative random variables. \n \n \n
URL:http://math.bas.bg/en/event/national-seminar-on-probability-and-statistics-2/
LOCATION:Institute of Mathematics and Informatics\, BAS\, Akad.G.Bonchev St\, bl. 8\, 1113\, Sofia\, Bulgaria
CATEGORIES:Regular Seminar
ORGANIZER;CN="Department%20of%20Operations%20Research%2C%20Probability%20and%20Statistics":MAILTO:jeni@math.bas.bg;
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