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>. 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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. Ergodic properties for $\alpha$-CIR models and a class of generalized Fleming-Viot processes http://ejp.ejpecp.org/article/view/2928 We discuss a Markov jump process regarded as a variant of the CIR (Cox-Ingersoll-Ross) model and its infinite-dimensional extension. These models belong to a class of measure-valued branching processes with immigration, whose jump mechanisms are governed by certain stable laws. The main result gives a lower spectral gap estimate for the generator. As an application, a certain ergodic property is shown for the generalized Fleming-Viot process obtained as the time-changed ratio process. Kenji Handa 2014-07-24 2014-07-24 19 The evolving beta coalescent http://ejp.ejpecp.org/article/view/3332 In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time.  As the population evolves over time, the tree that represents the genealogy of the population also changes, leading to a tree-valued stochastic process known as the evolving coalescent.  Here we will consider the evolving coalescent for populations whose genealogy can be described by a beta coalescent, which is known to give the genealogy of populations with very large family sizes.  We show that as the size of the population tends to infinity, the evolution of certain functionals of the beta coalescent, such as the total number of mergers, the total branch length, and the total length of external branches, converges to a stationary stable process.  Our methods also lead to new proofs of known asymptotic results for certain functionals of the non-evolving beta coalescent. Götz Kersting Jason Schweinsberg Anton Wakolbinger 2014-07-20 2014-07-20 19 On the exit time from a cone for brownian motion with drift http://ejp.ejpecp.org/article/view/3169 We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in particular that its exponential decreasing rate is a function of the distance between the drift and the cone, whereas the polynomial part in the asymptotics depends on the position of the drift with respect to the cone and its polar cone, and reflects the local geometry of the cone at the points that minimize the distance to the drift. Rodolphe Garbit Kilian Raschel 2014-07-20 2014-07-20 19 A population model with non-neutral mutations using branching processes with immigration http://ejp.ejpecp.org/article/view/2939 We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given by a constant mutation rate measure. We determine some genealogical properties of this process such as: distribution of the time to the most recent common ancestor (MRCA), bottleneck effect at the time to the MRCA (which might be drastic for some mutation rate measures), favorable type for the MRCA, asymptotics of the number of ancestors. Hongwei Bi Jean-Francois Delmas 2014-07-20 2014-07-20 19 Multidimensional fractional advection-dispersion equations and related stochastic processes http://ejp.ejpecp.org/article/view/2854 In this paper we study multidimensional fractional advection-dispersion equations involving fractional directional derivatives both from a deterministic and a stochastic point of view. For such equations we show the connection with a class of multidimensional Lévy processes. We introduce a novel Lévy-Khinchine formula involving fractional gradients and study the corresponding infinitesimal generator of multi-dimensional random processes. We also consider more general fractional transport equations involving Frobenius-Perron operators and their stochastic solutions. Finally, some results about fractional power of second order directional derivatives and their applications are also provided. Mirko D'Ovidio Roberto Garra 2014-07-12 2014-07-12 19