Electronic Communications in Probability 2014-04-15T01:47:19-07:00 Anton Bovier (Chief Editor) Open Journal Systems The Electronic Journal of Probability applies the <a href="" 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. <p><strong></strong>The <strong>Electronic Communications in Probability</strong> (ECP) publishes short research articles in probability theory. Its sister journal, the <a href="" 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="">Institute of Mathematical Statistics</a> (IMS) and the <a href=""> Bernoulli Society</a>. This web site uses the <a href="">Open Journal System</a> (OJS) free software developed by the non-profit organization <a href="">Public Knowledge Project</a> (PKP).</p><p>Please consider donating to the <a href="" target="_blank">Open Access Fund</a> of the IMS at this <a href="" target="_blank"><strong>page</strong></a> to keep the journal free.</p> On a dyadic approximation of predictable processes of finite variation 2014-04-15T01:47:19-07:00 Pietro Siorpaes <p>We show that any càdlàg predictable process of finite variation is an a.s. limit of elementary predictable processes; it follows that predictable stopping times can be approximated "from below" by predictable stopping times which take finitely many values. We then obtain as corollaries two classical theorems: predictable stopping times are announceable, and an increasing process is predictable iff it is natural.</p> 2014-04-15T01:47:05-07:00 The travel time in a finite box in supercritical Bernoulli percolation 2014-04-15T01:47:19-07:00 Raphaël Cerf We consider the standard site percolation model on the three dimensional cubic lattice. Starting solely with the hypothesis that $\theta(p)&gt;0$, we prove that, for any $\alpha&gt;0$, there exists $\kappa&gt;0$ such that, with probability larger than $1-1/n^\alpha$, every pair of sites inside the box $\Lambda(n)$ are joined by a path having at most $\kappa(\ln n)^2$ closed sites. 2014-04-12T03:39:34-07:00 Erratum: A note on Kesten's Choquet-Deny lemma 2014-04-15T01:47:19-07:00 Sebastian Mentemeier <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p>This is an erratum for <strong><a href="/article/view/2629" target="_self">ECP volume 18 paper 65 (2013)</a></strong>. In Proposition 3.1, Condition (C) does not imply that the set Λ(Γ) generates a dense subgroup of R. This has to be made an assumption. Alternatively, one can assume that the matrices are invertible.</p></div></div></div> 2014-03-19T02:21:29-07:00 Hedging of game options under model uncertainty in discrete time 2014-04-15T01:47:19-07:00 Yan Dolinsky We introduce a setup of model uncertaintyin discrete time. In this setup wederive dual expressions for the super-replication prices of game options with upper semicontinuous payoffs. We show that the super-replication price is equal to the supremum over a special (non dominated) set of martingale measures, of the corresponding Dynkin games values. This type of results is also new for American options. 2014-03-16T04:49:40-07:00 Law of large numbers for critical first-passage percolation on the triangular lattice 2014-04-15T01:47:19-07:00 Chang-Long Yao We study the site version of (independent) first-passage percolation on the triangular lattice $T$.  Denote the passage time of the site $v$ in $T$ by $t(v)$, and assume that $\mathbb{P}(t(v)=0)=\mathbb{P}(t(v)=1)=1/2$.  Denote by $a_{0,n}$ the passage time from 0 to (n,0), and by b_{0,n} the passage time from 0 to the halfplane $\{(x,y) : x\geq n\}$.  We prove that there exists a constant $0&lt;\mu&lt;\infty$ such that as $n\rightarrow\infty$, $a_{0,n}/\log n\rightarrow \mu$ in probability and $b_{0,n}/\log n\rightarrow \mu/2$ almost surely.  This result confirms a prediction of Kesten and Zhang<strong></strong>.  The proof relies on the existence of the full scaling limit of critical site percolation on $T$, established by Camia and Newman. 2014-03-15T05:45:34-07:00