A functional CLT for the occupation time of a state-dependent branching random walk

We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension $d\ge 3$, started off either from a Poisson field or in equilibrium, when suitably normalized, converges to a Brownian motion in $d\ge4$. In $d=3$, the limit process is a fractional Brownian motion with Hurst parameter 3/4 when starting in equilibrium, and a related Gaussian process when starting from a Poisson field. For (dependent) branching random walks with state dependent branching rate we obtain convergence in f.d.d. to the same limit process, and for $d=3$ also a functional limit theorem.Comment: Published in at http://dx.doi.org/10.1214/009117907000000150 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A COMPARISON OF EXTENDED SOURCE-FILTER MODELS FOR MUSICAL SIGNAL RECONSTRUCTION

China Scholarship Council (CSC)/ Queen Mary Joint PhD scholarship; Royal Academy of Engineering Research Fellowshi

Conceptual Truth Defended

Philosophers often rely on hypothetical scenarios to establish claims about causation, consciousness, knowledge, and the like. Consider e.g. this line of thought: (1) Knowledge is not justified true belief. Just contemplate the scenarios Gettier (1963) puts forth. In the situations Gettier describes, we find a protagonist having a true justified belief that p – but he still does not know that p. This is a paradigmatic instance of what I call scenario-based reasoning. In (1), Gettier’s scenarios are brought up to justify a claim about knowledge. Contemplating the situations Gettier describes is taken to somehow show, first, that this holds true: (2) Someone could be in a Gettier-style situation. Contemplating the Gettier-cases is, secondly, assumed to establish a rather substantial counterfactual conditional, to wit: (3) If someone were in a Gettier-style situation, she would have justified true belief, but she would still lack knowledge. Since (2) and (3) entail that someone could have justified true belief but no knowledge, we may conclude that knowledge cannot be justified true belief. In much the same vein

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Prof. Dr. N. NavabTo my familyAcknowledgements I am deeply grateful that I had the opportunity to write this thesis while working at the Chair for Pattern Recognition within the project B6 of the Sonderforschungsbereich 603 (funded by Deutsche Forschungsgemeinschaft). Many people contributed to this work and I want to express my gratitude to all of them