Researcher:
Öz, Mehmet

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PhD Student

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Mehmet

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Öz

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Öz, Mehmet

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2013 - 20173

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Researcher Of Publications: search.filters.isAuthorOfPublication.c407d302-13fb-4379-aaea-02e611d83683

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    Survival of branching Brownian motion in a uniform trap field
    (Elsevier Science Bv, 2016) N/A; Department of Mathematics; Öz, Mehmet; PhD Student; Department of Mathematics; Graduate School of Sciences and Engineering; N/A
    We study a branching Brownian motion Z evolving in R-d, where a uniform field of Poissonian traps are present. We consider a general offspring distribution for Z and find the asymptotic decay rate of the annealed survival probability, conditioned on non-extinction. The method of proof is to use a skeleton decomposition for the Galton-Watson process underlying Z and to show that the particles of finite line of descent do not contribute to the survival asymptotics. This work is a follow-up to Oz and Caglar (2013) and solves the problem considered therein completely.
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    Conditional speed of branching brownian motion, skeleton decomposition and application to random obstacles
    (Institute Henri Poincaré (IHP), 2017) Englander, Janos; Department of Mathematics; Öz, Mehmet; Çağlar, Mine; PhD. Student; Faculty Member; Department of Mathematics; College of Sciences; N/A; 105131
    We study a branching Brownian motion Z in Rd, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the whole motion when hit by a particle. Considering a general offspring distribution, we derive the decay rate of the annealed probability that none of the particles of Z hits a trap, asymptotically in time t. This proves to be a rich problem motivating the proof of a more general result about the speed of branching Brownian motion conditioned on non-extinction. We provide an appropriate "skeleton" decomposition for the underlying Galton-Watson process when supercritical and show that the "doomed" particles do not contribute to the asymptotic decay rate.
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    Tail probability of avoiding Poisson traps for branching Brownian motion
    (Elsevier, 2013) Department of Mathematics; Öz, Mehmet; Çağlar, Mine; PhD. Student; Faculty Member; Department of Mathematics; College of Sciences; N/A; 105131
    We consider a branching Brownian motion Z with exponential branching times and general offspring distribution evolving in R-d, where Poisson traps are present. A Poisson trap configuration with radius a is defined to be the random subset K of R-d given by K = boolean OR(x)l(,is an element of supp)(M) (B) over bar (x(i), a), where M is a Poisson random measure on B(R-d) with constant trap intensity. Survival up to time t is defined to be the event {T > t) with T = inf{s >= 0 : Z(s)(K) > 0} being the first trapping time. Following the work of Englander (2000), Englander and den Hollander (2003), where strictly dyadic branching is considered, we consider here a general offspring distribution for Z and settle the problem of survival asymptotics for the system.