Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

Multivariate fractional Poisson processes and compound sums

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (nonfractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes

Large deviations for i.i.d. replications of the total progeny of a Galton--Watson process

The Galton--Watson process is the simplest example of a branching process. The relationship between the offspring distribution, and, when the extinction occurs almost surely, the distribution of the total progeny is well known. In this paper, we illustrate the relationship between these two distributions when we consider the large deviation rate function (provided by Cram\'{e}r's theorem) for empirical means of i.i.d. random variables. We also consider the case with a random initial population. In the final part, we present large deviation results for sequences of estimators of the offspring mean based on i.i.d. replications of total progeny.Comment: Published at http://dx.doi.org/10.15559/16-VMSTA72 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/

MOND and IMF variations in early-type galaxies from ATLAS3D

MOdified Newtonian dynamics (MOND) represents a phenomenological alternative to dark matter (DM) for the missing mass problem in galaxies and clusters of galaxies. We analyze the central regions of a local sample of $\sim 220$ early-type galaxies from the $\rm ATLAS^{3D}$ survey, to see if the data can be reproduced without recourse to DM. We estimate dynamical masses in the MOND context through Jeans analysis, and compare to $\rm ATLAS^{3D}$ stellar masses from stellar population synthesis. We find that the observed stellar mass--velocity dispersion relation is steeper than expected assuming MOND with a fixed stellar initial mass function (IMF) and a standard value for the acceleration parameter $a_{\rm 0}$. Turning from the space of observables to model space, a) fixing the IMF, a universal value for $a_{\rm 0}$ cannot be fitted, while, b) fixing $a_{\rm 0}$ and leaving the IMF free to vary, we find that it is "lighter" (Chabrier-like) for low-dispersion galaxies, and "heavier" (Salpeter-like) for high dispersions. This MOND-based trend matches inferences from Newtonian dynamics with DM, and from detailed analysis of spectral absorption lines, adding to the converging lines of evidence for a systematically-varying IMF.Comment: 6 pages, 3 figures, accepted for publication on MNRAS Letters, typos corrected and further references adde

Asymptotic results for random flights

The random flights are (continuous time) random walkswith finite velocity. Often, these models describe the stochastic motions arising in biology. In this paper we study the large time asymptotic behavior of random flights. We prove the large deviation principle for conditional laws given the number of the changes of direction, and for the non-conditional laws of some standard random flights.Comment: 3 figure

Multivariate fractional Poisson processes and compound sums

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.Comment: 19 pages Keywords: conditional independence, Fox-Wright function, fractional differential equations, random time-chang

The impact of soil and vegetation management on ecosystem services in european almond orchards

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Large deviations for fractional Poisson processes

We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance model with constant premium rate, i.i.d. light tail claim sizes, and a fractional Poisson claim number process. We conclude with the alternative version where all the random variables are weighted Poisson distributed. Keywords: Mittag Leffler function; renewal process; random time ch