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Wed, 29 Jan 2014 14:17:28 +0100Wed, 29 Jan 2014 14:17:28 +0100Delay equations driven by rough paths
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32895
In this article, we illustrate the flexibility of the algebraic integration formalism introduced in M. Gubinelli (2004), Controlling Rough Paths, J. Funct. Anal. 216, 86-140, by establishing an existence and uniqueness result for delay equations driven by rough paths. We then apply our results to the case where the driving path is a fractional Brownian motion with Hurst parameter H > 1/3.
Andreas Neuenkirch; Ivan Nourdin; Samy Tindelarticlehttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32895Wed, 29 Jan 2014 14:17:28 +0100A Gaussian limit process for optimal FIND algorithms
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32751
We consider versions of the FIND algorithm where the pivot element used is the median of a subset chosen uniformly at random from the data. For the median selection we assume that subsamples of size asymptotic to c⋅nα are chosen, where 0<α≤12, c>0 and n is the size of the data set to be split. We consider the complexity of FIND as a process in the rank to be selected and measured by the number of key comparisons required. After normalization we show weak convergence of the complexity to a centered Gaussian process as n→∞, which depends on α. The proof relies on a contraction argument for probability distributions on càdlàg functions. We also identify the covariance function of the Gaussian limit process and discuss path and tail properties.Henning Sulzbach; Ralph Neininger; Michael Drmotaarticlehttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32751Mon, 27 Jan 2014 09:23:17 +0100