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>. This web site uses the <a href="http://en.wikipedia.org/wiki/Open_Journal_Systems">Open Journal System</a> (OJS) free software developed by the non-profit organization <a href="http://en.wikipedia.org/wiki/Public_Knowledge_Project">Public Knowledge Project</a> (PKP).</p><p>Please consider donating to the <a href="http://www.imstat.org/publications/open.htm" target="_blank">Open Access Fund</a> of the IMS at this <a href="https://secure.imstat.org/secure/orders/donations.asp" target="_blank"><strong>page</strong></a> to keep the journal free.</p>en-USElectronic Communications in Probability1083-589XThe Electronic Journal of Probability applies the <a href="http://creativecommons.org/licenses/by/2.5/legalcode" target="_blank">Creative Commons Attribution License</a> (CCAL) to all articles we publish in this journal. 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 Note on the $S_2(\delta)$ Distribution and the Riemann Xi Function
http://ecp.ejpecp.org/article/view/3608
The theory of $S_2(\delta)$ family of probability distributions is used to give a derivation of the functional equation of the Riemann xi function. The $\delta$ deformation of the xi function is formulated in terms of the $S_2(\delta)$ distribution and shown to satisfy Riemann's functional equation. Criteria for simplicity of roots of the xi function and for its simple roots to satisfy the Riemann hypothesis are formulated in terms of a differentiability property of the $S_2(\delta)$ family. For application, the values of the Riemann zeta function at the integers and of the Riemann xi function in the complex plane are represented as integrals involving the Laplace transform of $S_2.$Dmitry Ostrovsky2014-12-112014-12-1119On the range of subordinators
http://ecp.ejpecp.org/article/view/3629
In this note we look into detail into the box-counting dimension of subordinators. Given that X is a non-decreasing Levy process which is not Compound Poisson process we show that in the limit, a.s., the minimum number of boxes of size $a$ that cover the range of $(X_s)_{s\leq t}$ is a.s. of order $t/U(a)$, where U is the potential function of X. This is a more rened result than the lower and upper index of the box-counting dimension computed by Jean Bertoin in his 1999 book, which deals with the asymptotic of the number of boxes at logarithmic scale.Mladen Svetoslavov Savov2014-12-112014-12-1119Lower bounds on the smallest eigenvalue of a sample covariance matrix.
http://ecp.ejpecp.org/article/view/3807
We provide tight lower bounds on the smallest eigenvalue of a sample covariance matrix of a centred isotropic random vector under weak or no assumptions on its components.Pavel Yaskov2014-12-062014-12-0619Large gaps asymptotics for the 1-dimensional random Schr¨odinger operator
http://ecp.ejpecp.org/article/view/2724
We show that in the Schr\"{o}dinger point process, Sch$_\tau$, $\tau>0,$ the probability of having no eigenvalue in a fixed interval of size $\lambda$ is given by <br />\[ <br />\exp\left(-\frac{\lambda^2}{4\tau}+\left(\frac{2}{\tau}-\frac{1}{4}\right)\lambda +o(\lambda)\right), <br />\] <br />as $\lambda\to\infty.$ It is a slightly more precise version than the one given in a previous work.Stephanie S.M. Jacquot2014-11-262014-11-2619A note on the strong formulation of stochastic control problems with model uncertainty
http://ecp.ejpecp.org/article/view/3436
We consider a Markovian stochastic control problem with model uncertainty. The controller (intelligent player) observes only the state, and, therefore, uses feedback (closed-loop) strategies. The adverse player (nature) who does not have a direct interest in the payoff, chooses open-loop controls that parametrize Knightian uncertainty. This creates a two-step optimization problem (like half of a game) over feedback strategies and open-loop controls. The main result is to show that, under some assumptions, this provides the same value as the (half of) the zero-sum symmetric game where the adverse player also plays feedback strategies and actively tries to minimize the payoff. The value function is independent of the filtration accessible to the adverse player. Aside from the modeling issue, the present note is a technical companion to a previous work.Mihai Sirbu2014-11-262014-11-2619