TY - JOUR A1 - Conforti, Giovanni A1 - Roelly, Sylvie T1 - Bridge mixtures of random walks on an Abelian group JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability KW - random walk on Abelian group KW - reciprocal class KW - stochastic bridge Y1 - 2017 U6 - https://doi.org/10.3150/15-BEJ783 SN - 1350-7265 SN - 1573-9759 VL - 23 SP - 1518 EP - 1537 PB - International Statistical Institute CY - Voorburg ER - TY - JOUR A1 - Cotronei, Mariantonia A1 - Di Salvo, Rosa A1 - Holschneider, Matthias A1 - Puccio, Luigia T1 - Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes JF - Journal of computational and applied mathematics N2 - In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered. KW - Subdivision schemes KW - Interpolation KW - Simulation of Gaussian processes KW - Bayesian inversion Y1 - 2016 U6 - https://doi.org/10.1016/j.cam.2016.08.002 SN - 0377-0427 SN - 1879-1778 VL - 311 SP - 342 EP - 353 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Dereudre, David A1 - Mazzonetto, Sara A1 - Roelly, Sylvie T1 - Exact simulation of Brownian diffusions with drift admitting jumps JF - SIAM journal on scientific computing N2 - In this paper, using an algorithm based on the retrospective rejection sampling scheme introduced in [A. Beskos, O. Papaspiliopoulos, and G. O. Roberts,Methodol. Comput. Appl. Probab., 10 (2008), pp. 85-104] and [P. Etore and M. Martinez, ESAIM Probab.Stat., 18 (2014), pp. 686-702], we propose an exact simulation of a Brownian di ff usion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical di ffi culty due to the presence of t w o jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift. KW - exact simulation methods KW - skew Brownian motion KW - skew diffusions KW - Brownian motion with discontinuous drift Y1 - 2017 U6 - https://doi.org/10.1137/16M107699X SN - 1064-8275 SN - 1095-7197 VL - 39 IS - 3 SP - A711 EP - A740 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Dereudre, David A1 - Roelly, Sylvie T1 - Path-dependent infinite-dimensional SDE with non-regular drift BT - an existence result JF - Annales de l'Institut Henri Poincaré : B, Probability and statistics N2 - We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither bounded or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy and a finite second moment. The originality of our method leads in the use of the specific entropy as a tightness tool and in the description of such infinite-dimensional stochastic process as solution of a variational problem on the path space. Our result clearly improves previous ones obtained for free dynamics with bounded drift. N2 - Nous établissons, dans cet article, l’existence de solutions faibles pour un système infini-dimensionnel de diffusions browniennes. Le terme de dérive est véritablement général, au sens où il est supposé n’être ni borné, ni continu, ni Markovien. Nous supposons cependant que la loi initiale admet une entropie spécifique finie. L’originalité de notre méthode consiste en l’utilisation de la bornitude de l’entropie spécifique comme critère de tension et en l’identification des solutions du système comme solutions d’un problème variationnel sur l’espace des trajectoires. Notre résultat améliore clairement ceux préexistants concernant des dynamiques libres perturbées par des dérives bornées. KW - Infinite-dimensional SDE KW - Non-Markov drift KW - Non-regular drift KW - Variational principle KW - Specific entropy Y1 - 2017 U6 - https://doi.org/10.1214/15-AIHP728 SN - 0246-0203 VL - 53 IS - 2 SP - 641 EP - 657 PB - Inst. of Mathematical Statistics CY - Bethesda ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Fernandes, Vitor H. A1 - Koppitz, Jörg T1 - A note on generators of the endomorphism semigroup of an infinite countable chain JF - Journal of Algebra and its Applications N2 - In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X. KW - Infinite chain KW - endomorphism semigroup KW - generators KW - relative rank Y1 - 2016 U6 - https://doi.org/10.1142/S0219498817500311 SN - 0219-4988 SN - 1793-6829 VL - 16 IS - 2 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On the semigroup of all partial fence-preserving injections on a finite set JF - Journal of Algebra and Its Applications N2 - For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn; 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi. KW - Quasilinear equations KW - Removable sets KW - Porous medium equation Y1 - 2017 U6 - https://doi.org/10.1007/s40590-017-0169-3 SN - 1405-213X SN - 2296-4495 VL - 24 IS - 2 SP - 427 EP - 437 PB - Springer CY - Cham ER - TY - JOUR A1 - Gairing, Jan A1 - Högele, Michael A1 - Kosenkova, Tetiana T1 - Transportation distances and noise sensitivity of multiplicative Levy SDE with applications JF - Stochastic processes and their application N2 - This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate. KW - Stochastic differential equations KW - Multiplicative Levy noise KW - Levy type processes KW - Heavy-tailed distributions KW - Model selection KW - Wasserstein distance KW - Time series Y1 - 2017 U6 - https://doi.org/10.1016/j.spa.2017.09.003 SN - 0304-4149 SN - 1879-209X VL - 128 IS - 7 SP - 2153 EP - 2178 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Gairing, Jan M. A1 - Hogele, Michael A. A1 - Kosenkova, Tania A1 - Monahan, Adam H. T1 - How close are time series to power tail Levy diffusions? JF - Chaos : an interdisciplinary journal of nonlinear science N2 - This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as a-stable Levy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular, they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition, this approach gives evidence for heavy tails in datasets of precipitable water vapor of the Western Tropical Pacific. Published by AIP Publishing. Y1 - 2017 U6 - https://doi.org/10.1063/1.4986496 SN - 1054-1500 SN - 1089-7682 VL - 27 PB - American Institute of Physics CY - Melville ER -