Electronic Communications in Probability http://ecp.ejpecp.org/ <p><strong></strong>The <strong>Electronic Communications in Probability</strong> (ECP) publishes short research articles in probability theory. Its sister journal, the <a href="http://ejp.ejpecp.org/" target="_self">Electronic Journal of Probability</a> (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.</p><p>EJP and ECP are free access official journals of the <a href="http://www.imstat.org/">Institute of Mathematical Statistics</a> (IMS) and the <a href="http://isi.cbs.nl/BS/bshome.htm"> Bernoulli Society</a>. 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Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.<br /><br /><strong>Summary of the Creative Commons Attribution License</strong><br /><br />You are free<br /><ul><li> to copy, distribute, display, and perform the work</li><li> to make derivative works</li><li> to make commercial use of the work</li></ul>under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author. A counter example to central limit theorem in Hilbert spaces under a strong mixing condition http://ecp.ejpecp.org/article/view/3249 We show that in a separable infinite dimensional Hilbert space, uniform integrability of the square of the norm of normalized partial sums of a strictly stationary sequence, together with a strong mixing condition, does not guarantee the central limit theorem. Davide Giraudo Dalibor Volny 2014-08-29 2014-08-29 19 A connection of the Brascamp-Lieb inequality with Skorokhod embedding http://ecp.ejpecp.org/article/view/3025 We reveal a connection of the Brascamp-Lieb inequality with Skorokhod embedding. Error bounds for the inequality in terms of the variance are also provided. Yuu Hariya 2014-08-29 2014-08-29 19 On functional weak convergence for partial sum processes http://ecp.ejpecp.org/article/view/3686 For a strictly stationary sequence of regularly varying random variables we study functional weak convergence of partial sum processes in the space $D[0,1]$ with the $J_{1}$ topology. Under the strong mixing condition, we identify necessary and sufficient conditions for such convergence in terms of the corresponding extremal index. We also give conditions under which the regular variation property is a necessary condition for this functional convergence in the case of weak dependence. Danijel Krizmanic 2014-08-26 2014-08-26 19 Concentration of random polytopes around the expected convex hull http://ecp.ejpecp.org/article/view/3376 We provide a streamlined proof and improved estimates for the weak multivariate Gnedenko law of large numbers on concentration of random polytopes within the space of convex bodies (in a fixed or a high dimensional setting), as well as a corresponding strong law of large numbers. Daniel J. Fresen Richard A. Vitale 2014-08-26 2014-08-26 19 Weak and strong solutions of general stochastic models http://ecp.ejpecp.org/article/view/2833 Typically, a stochastic model relates stochastic “inputs” and, perhaps, controls tostochastic “outputs”. A general version of the Yamada-Watanabe and Engelbert the-orems relating existence and uniqueness of weak and strong solutions of stochasticequations is given in this context. A notion of compatibility between inputs and out-puts is critical in relating the general result to its classical forebears. The usualformulation of stochastic differential equations driven by semimartingales does notrequire compatibility, so a notion of partial compatibility is introduced which doeshold. Since compatibility implies partial compatibility, classical strong uniquenessresults imply strong uniqueness for compatible solutions. Weak existence argumentstypically give existence of compatible solutions (not just partially compatible solu-tions), and as in the original Yamada-Watanabe theorem, existence of strong solutionsfollows. Thomas G. Kurtz 2014-08-25 2014-08-25 19