TY - JOUR A1 - Cattiaux, Patrick A1 - Fradon, Myriam A1 - Kulik, Alexei M. A1 - Roelly, Sylvie T1 - Long time behavior of stochastic hard ball systems JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability N2 - We study the long time behavior of a system of n = 2, 3 Brownian hard balls, living in R-d for d >= 2, submitted to a mutual attraction and to elastic collisions. KW - hard core interaction KW - local time KW - Lyapunov function KW - normal reflection KW - Poincare inequality KW - reversible measure KW - stochastic differential equations Y1 - 2016 U6 - https://doi.org/10.3150/14-BEJ672 SN - 1350-7265 SN - 1573-9759 VL - 22 SP - 681 EP - 710 PB - International Statistical Institute CY - Voorburg ER - TY - JOUR A1 - Conforti, Giovanni A1 - Kosenkova, Tetiana A1 - Roelly, Sylvie T1 - Conditioned Point Processes with Application to Levy Bridges JF - Journal of theoretical probability N2 - Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke’s formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump Lévy process in Rd with a height a can be interpreted as a Poisson point process on space–time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of Lévy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample Lévy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein–Uhlenbeck processes driven by Lévy noise. KW - Ornstein-Uhlenbeck Y1 - 2019 U6 - https://doi.org/10.1007/s10959-018-0863-8 SN - 0894-9840 SN - 1572-9230 VL - 32 IS - 4 SP - 2111 EP - 2134 PB - Springer CY - New York ER - TY - JOUR A1 - Conforti, Giovanni A1 - Leonard, Christian A1 - Murr, Rüdiger A1 - Roelly, Sylvie T1 - Bridges of Markov counting processes. Reciprocal classes and duality formulas JF - Electronic communications in probability N2 - Processes sharing the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula. KW - Counting process KW - bridge KW - reciprocal class KW - duality formula Y1 - 2015 U6 - https://doi.org/10.1214/ECP.v20-3697 SN - 1083-589X VL - 20 PB - Univ. of Washington, Mathematics Dep. CY - Seattle ER - TY - JOUR A1 - Conforti, Giovanni A1 - Pra, Paolo Dai A1 - Roelly, Sylvie T1 - Reciprocal Class of Jump Processes JF - Journal of theoretical probability N2 - Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set . We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state. KW - Reciprocal processes KW - Stochastic bridges KW - Jump processes KW - Compound Poisson processes Y1 - 2015 U6 - https://doi.org/10.1007/s10959-015-0655-3 SN - 0894-9840 SN - 1572-9230 VL - 30 SP - 551 EP - 580 PB - Springer CY - New York ER - 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 - 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 - Dombrowsky, Charlotte A1 - Und, Myriam Fradon A1 - Roelly, Sylvie T1 - Packungen aus Kreisscheiben BT - Wie eine wahrscheinlichkeitstheoretische Sichtweise eine geometrische Analyse vervollständigen kann JF - Elemente der Mathematik N2 - Der englische Seefahrer Sir Walter Raleigh fragte sich einst, wie er in seinem Schiffsladeraum moeglichst viele Kanonenkugeln stapeln koennte. Johannes Kepler entwickelte daraufhin 1611 eine Vermutung ueber die optimale Anordnung der Kugeln. Diese Vermutung sollte sich als eine der haertesten mathematischen Nuesse der Geschichte erweisen. Selbst in der Ebene sind dichteste Packungen kongruenter Kreise eine Herausforderung. 1892 und 1910 veroeffentlichte Axel Thue (kritisierte) Beweise, dass die hexagonale Kreispackung optimal sei. Erst 1940 lieferte Laszlo Fejes Toth schliesslich einen wasserdichten Beweis fuer diese Tatsache. Eine Variante des Problems verlangt, Packungen mit endlich vielen kongruenten Kugeln zu finden, die eine gewisse quadratische Energie minimieren: Diese spannende geometrische Aufgabe wurde 1967 von Toth gestellt. Sie ist auch heute noch nicht vollstaendig gelaest. In diesem Beitrag schlagen die Autorinnen eine originelle wahrscheinlichkeitstheoretische Methode vor, um in der Ebene Näherungen der Lösung zu konstruieren. Y1 - 2019 U6 - https://doi.org/10.4171/EM/381 SN - 0013-6018 SN - 1420-8962 VL - 74 IS - 2 SP - 45 EP - 62 PB - EMS Publ. CY - Zürich ER - TY - JOUR A1 - Fradon, Myriam A1 - Roelly, Sylvie T1 - Infinitely many Brownian globules with Brownian radii N2 - We consider an infinite system of non-overlapping globules undergoing Brownian motions in R-3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional stochastic differential equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures. Y1 - 2010 UR - http://www.worldscinet.com/sd/sd.shtml U6 - https://doi.org/10.1142/S021949371000311x SN - 0219-4937 ER - TY - JOUR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - On time duality for Markov Chains JF - Stochastic models N2 - For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are in time duality. We introduce a new condition called permuted balance that generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided. KW - Time duality KW - Detailed balance KW - First passage time KW - Reversibility KW - Permuted balance KW - Markov chain Y1 - 2015 U6 - https://doi.org/10.1080/15326349.2014.969736 SN - 1532-6349 SN - 1532-4214 VL - 31 IS - 1 SP - 98 EP - 118 PB - Taylor & Francis Group CY - Philadelphia ER -