Electronic Communications in Probability 2014-10-20T19:42:18-07:00 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. 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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> Stochastic Perron's method for optimal control problems with state constraints 2014-10-20T19:42:18-07:00 Dmitry B. Rokhlin We apply the stochastic Perron method of Bayraktar and Sîrbu to a general infinite horizon optimal control problem, where the state $X$ is a controlled diffusion process, and the state constraint is described by a closed set. We prove that the value function $v$ is bounded from below (resp., from above) by a viscosity supersolution (resp., subsolution) of the related state constrained problem for the Hamilton-Jacobi-Bellman equation. In the case of a smooth domain, under some additional assumptions, these estimates allow to identify $v$ with a unique continuous constrained viscosity solution of this equation. 2014-10-20T19:42:00-07:00 A multidimensional version of noise stability 2014-10-20T19:42:18-07:00 Joe Neeman We give a multivariate generalization of Borell's noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process. 2014-10-20T00:44:22-07:00 Erratum: Transience and recurrence of rotor-router walks on directed covers of graphs 2014-10-20T19:42:18-07:00 Ecaterina Sava-Huss Wilfried Huss In the paper "Transience and recurrence of rotor-router walks on directed covers of graphs", published in <a href="">ECP volume 17 (2012), no. 41</a> there is an error in the proof of Corollary 3.8. This corollary is essential for the transient part in the proof of Theorem 3.5(b). We fix this error by constructing a new rotor-router process, which fulfills our needs, and for which the statement of Corollary 3.8. holds. 2014-10-10T02:49:16-07:00 Conditional persistence of Gaussian random walks 2014-10-20T19:42:18-07:00 Fuchang Gao Zhenxia Liu Xiangfeng Yang Let $\{X_n\}_{n\geq1}$ be a sequence of i.i.d. standard Gaussian random variables, let $S_n=\sum_{i=1}^nX_i$ be the Gaussian random walk, and let $T_n=\sum_{i=1}^nS_i$ be the integrated (or iterated) Gaussian random walk. In this paper we derive the following upper and lower bounds for the conditional persistence:$$\mathbb{P}\left\{\max_{1\leq k \leq n}T_{k} \leq 0\,\,\Big|\,\,T_n=0,S_n=0\right\}\lesssim n^{-1/2},\ \mathbb{P}\left\{\max_{1\leq k \leq 2n}T_{k} \leq 0\,\,\Big|\,\,T_{2n}=0,S_{2n}=0\right\}\gtrsim\frac{n^{-1/2}}{\log n},$$for $n\rightarrow\infty,$ which partially proves a conjecture by Caravenna and Deuschel (2008). 2014-10-10T02:39:56-07:00 A renewal version of the Sanov theorem 2014-10-20T19:42:18-07:00 Mauro Mariani Lorenzo Zambotti Large deviations for the local time of a process <span>X(</span><span>t) </span><span>are investigated, where X(t)=xi for t∈[Si-1,Si[ and (x_j) are i.i.d. random variables on a Polish space, S_j is the j-th arrival time of a renewal process depending on (x_j). No moment conditions are assumed on the arrival times of the renewal process.</span> 2014-10-08T23:42:03-07:00