Electronic Journal of Probability
http://ejp.ejpecp.org/
<p><strong> </strong></p>The <strong>Electronic Journal of Probability</strong> (EJP) publishes full-length research articles in probability theory. Short papers, those less than 12 pages, should be submitted first to its sister journal, the <a href="http://ecp.ejpecp.org/" target="_blank">Electronic Communications in Probability</a> (ECP). EJP and ECP share the same editorial board, but with different Editors in Chief.<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 Journal of Probability1083-6489The 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.Fluctuation exponents for directed polymers in the intermediate disorder regime
http://ejp.ejpecp.org/article/view/3307
We derive exact fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate scaling regime. This regime corresponds to taking the inverse temperature to zero as the size of the system goes to infinity. The exponents satisfy the KPZ scaling relation and coincide with physical predictions.In the critical case, we recover the fluctuation exponent of the Hopf-Cole solution of the KPZ equation in equilibrium and close to equilibrium.Gregorio R. Moreno FloresTimo SeppäläinenBenedek Valkó2014-09-262014-09-2619Local probabilities for random walks with negative drift conditioned to stay nonnegative
http://ejp.ejpecp.org/article/view/3426
Let $S_n, n=0,1,...,$ with $S_0=0$ be a random walk with negative drift and let $\tau_x=\min\{k>0: S_k<-x\}, \, x\geq 0.$ Assuming that the distribution of i.i.d. increments of the random walk is absolutely continuous with subexponential density we find the asymptotic behavior, as $n\to\infty$ of the probabilities $\mathbf{P}(\tau_x=n)$ and $\mathbf{P}(S_n\in (y,y+\Delta],\tau_x>n)$ for fixed $x$ and various ranges of $y.$ The case of lattice distribution of increments is considered as well.Denis DenisovVladimir VatutinVitali Wachtel2014-09-262014-09-2619A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains
http://ejp.ejpecp.org/article/view/3216
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions which differs from the class F. This situation occurs in the case of data arising from dynamical systems or Markov chains, for which the Perron-Frobenius or Markov operator, respectively, has a spectral gap on a restricted space. We provide applications to iterative Lipschitz models that contract on average.Herold DehlingOlivier DurieuMarco Tusche2014-09-202014-09-2019A Gaussian process approximation for two-color randomly reinforced urns
http://ejp.ejpecp.org/article/view/3432
The Polya urn has been extensively studied and is widely applied in many disciplines. An important application is to use urn models to develop randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed. In this paper, we prove a Gaussian process approximation for the sequence of random composotions of a two-color randomly reinforced urn for both the cases with the equal and unequal reinforcement means. The Gaussian process is a tail stochastic integral with respect to a Brownian motion. By using the Gaussian approximation, the law of the iterated logarithm and the functional central limit theorem in both the stable convergence sense and the almost-sure conditional convergence sense are established. Also as a consequence, we are able to prove that the limit distribution of the normalized urn composition has no points masses both when the reinforcements means are equal and unequal under the assumption of only finite $(2+\epsilon)$-th moments.Lixin Zhang2014-09-182014-09-1819Small deviations for time-changed Brownian motions and applications to second-order chaos
http://ejp.ejpecp.org/article/view/2993
We prove strong small deviations results for Brownian motion under independent time-changes satisfying their own asymptotic criteria. We then apply these results to certain stochastic integrals which are elements of second-order homogeneous chaos.Daniel DobbsTai Melcher2014-09-162014-09-1619