2024 | Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect | M. Fradon, J. Kern, S. Roelly, A. ZassZeitschrift: Stochastic Processes and ApplicationsBand: 171Link zur Publikation
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Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect
Autoren: M. Fradon, J. Kern, S. Roelly, A. Zass
(2024)
We consider a random diffusion dynamics for an infinite system of hard spheres of two different sizes evolving in Rd, its reversible probability measure, and its projection on the subset of the large spheres. The main feature is the occurrence of an attractive short-range dynamical interaction – known in the physics literature as a depletion interaction – between the large spheres, which is induced by the hidden presence of the small ones. By
considering the asymptotic limit for such a system when the density of the particles is high, we also obtain a constructive dynamical approach to the famous discrete geometry problem of maximisation of the contact number of n identical spheres in Rd. As support material, we propose numerical simulations in the form of movies.
Zeitschrift:
Stochastic Processes and Applications
2023 | On reflected diffusions in cones and cylinders | Oleksii Kulyk, Andrey Pilipenko, Sylvie RoellyZeitschrift: Ukrains'kyi Matematychnyi ZhurnalSeiten: 1497-1521Band: 75 (11)Link zur Publikation
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On reflected diffusions in cones and cylinders
Autoren: Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly
(2023)
Let X be a diffusion in a cone with oblique reflection at the boundary. We study the question whether X reaches a vertex of the cone for a finite time with positive probability. We propose new probabilistic method of investigation connected with the long-term behavior of a diffusion reflected in a cylinder.
Zeitschrift:
Ukrains'kyi Matematychnyi Zhurnal
2023 | Übungsbuch zur Stochastik: Aufgaben und Lösungen. Grundlegende Konzepte und Anwendungen | T. Ehlen, A. Flöge, F. Göbel, P. Keller, S. RœllyVerlag: Universitätsverlag Potsdam, Hrsg.: P. Keller, S. RoellySeiten: 1-306Link zur Publikation
Übungsbuch zur Stochastik: Aufgaben und Lösungen. Grundlegende Konzepte und Anwendungen
Autoren: T. Ehlen, A. Flöge, F. Göbel, P. Keller, S. Rœlly
(2023)
Dieses Buch stellt Übungen zu den Grundbegriffen und Grundsätzen der Stochastik und ihre Lösungen zur Verfügung.
So wie man Tonleitern in der Musik trainiert, so berechnet man Übungsaufgaben in der Mathematik. In diesem Sinne soll dieses Übungsbuch vor allem als Vorlage dienen für das eigenständige, eigenverantwortliche Lernen und Üben.
Die Schönheit und Einzigartigkeit der Wahrscheinlichkeitstheorie besteht darin, dass sie eine Vielzahl von realen Phänomenen modellieren kann. Daher findet man hier Aufgaben mit Verbindungen zur Geometrie, zu Glücksspielen, zur Versicherungsmathematik, zur Demographie und vielen anderen Themen.
Die Zeichnerin Gisela Gurr hat einige Aufgaben des Buches mit Illustrationen bereichert.
Verlag:
Universitätsverlag Potsdam, Hrsg.: P. Keller, S. Roelly
2022 | Random population dynamics under catastrophic events | Patrick Cattiaux, Jens Fischer, Sylvie Roelly, Samuel SindayigayaZeitschrift: Journal of Applied ProbabilitySeiten: 962-982Band: 59 (4)Link zur Publikation
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Random population dynamics under catastrophic events
Autoren: Patrick Cattiaux, Jens Fischer, Sylvie Roelly, Samuel Sindayigaya
(2022)
In this paper we introduce new Birth-and-Death processes with partial catastrophe and study their properties. In particular we obtain some estimates for the mean catastrophe time, and the first and second moments of the distribution of the process at a fixed time t. This is completed by some asymptotic results.
Zeitschrift:
Journal of Applied Probability
2021 | Exponential a.s. synchronization of one-dimensional diffusions with non-regular coefficients | Olga Aryasova, Andrey Pilipenko, Sylvie RoellyZeitschrift: Stochastic Analysis and ApplicationsSeiten: 631-642Band: 39 (4)Link zur Publikation
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Exponential a.s. synchronization of one-dimensional diffusions with non-regular coefficients
Autoren: Olga Aryasova, Andrey Pilipenko, Sylvie Roelly
(2021)
We study the asymptotic behaviour of a real-valued diffusion whose non-
regular drift is given as a sum of a dissipative term and a bounded measurable one.
We prove that two trajectories of that diffusion converge a.s. to one another at an
exponential explicit rate as soon as the dissipative coefficient is large enough. A
similar result in Lp is obtained.
Zeitschrift:
Stochastic Analysis and Applications
2020 | Marked Gibbs point processes with unbounded interaction: an existence result | Sylvie Roelly, Alexander ZassZeitschrift: Journal of Statistical PhysicsSeiten: 972–996Band: 179Link zur Publikation
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Marked Gibbs point processes with unbounded interaction: an existence result
Autoren: Sylvie Roelly, Alexander Zass
(2020)
We construct marked Gibbs point processes in ℝd under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an as finite but random range. Secondly, the random marks - attached to the locations in ℝd - belong to a general normed space S. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.
Zeitschrift:
Journal of Statistical Physics
2020 | | Sylvie Roelly (Ed.)Reihe: Lectures in Pure and Applied MathematicsVerlag: Potsdam University PressBuchtitel: Proceedings of the XI international conference stochastic and analytic methods in mathematical physicsBand: 6Link zur Publikation
The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
Reihe:
Lectures in Pure and Applied Mathematics
Verlag:
Potsdam University Press
Buchtitel:
Proceedings of the XI international conference stochastic and analytic methods in mathematical physics
2020 | Pinned diffusions and Markov bridges | Florian Hildebrandt, Sylvie RoellyZeitschrift: Journal of Theoretical ProbabilitySeiten: 906-917Band: 33Link zur Publikation
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Pinned diffusions and Markov bridges
Autoren: Florian Hildebrandt, Sylvie Roelly
(2020)
In this article we consider a family of real-valued diffusion processes on the time interval [0; 1] indexed by their prescribed initial value and another point y in space. We first present a condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in y at time 1. Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an Ito diffusion? We eventually illustrate our precise answer with several examples.
Zeitschrift:
Journal of Theoretical Probability
2019 | Conditioned point processes with application to Lévy bridges | Giovanni Conforti, Tetiana Kosenkova, Sylvie RoellyZeitschrift: Journal of Theoretical ProbabilitySeiten: 2111-2134Band: 32Link zur Publikation
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Conditioned point processes with application to Lévy bridges
Autoren: Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly
(2019)
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to gain quantitative results about stochastic domination for Poisson point processes under linear constraints.
Since bridges of a pure jump Lévy process in R^d with a height h can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to h, 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 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.
Zeitschrift:
Journal of Theoretical Probability
2019 | 1940 : Wolfgang Döblin, génie du passé, héros d’aujourd’hui. Quand les probabilités rencontrent la physique et l’économie. | Guillaume Peter, Sylvie RoellyZeitschrift: Images des MathématiquesReihe: Les 80 ans du CNRSVerlag: Institut Henri PoincaréLink zur Publikation
1940 : Wolfgang Döblin, génie du passé, héros d’aujourd’hui. Quand les probabilités rencontrent la physique et l’économie.
Autoren: Guillaume Peter, Sylvie Roelly
(2019)
L’histoire ne se compose pas uniquement de guerres ou de règnes de monarques. La science a marqué l’histoire grâce à de nombreuses découvertes, passionnantes tant d’un point de vue scientifique qu’historique. Nous connaissons les grands de ce monde dont les découvertes ont façonné notre société : Pierre (1859-1906) et Marie (1867-1934) Curie, Albert Einstein (1879-1955), Nicolas Tesla (1856-1943), Ernest Rutherford (1871-1937) et bien d’autres encore. Wolfgang Döblin (1915-1940) mérite lui aussi toute notre attention car ses travaux mathématiques avant-gardistes sont méconnus, bien qu’ils aient débouché sur des applications importantes dans nombre de domaines tels la finance ou la physique. Sa vie tourmentée fut dense et finit tragiquement.
Zeitschrift:
Images des Mathématiques
Verlag:
Institut Henri Poincaré
2019 | Packungen aus Kreisscheiben | Charlotte Dombrowsky, Myriam Fradon, Sylvie RoellyZeitschrift: Elemente der MathematikSeiten: pp.45-62Band: 74-2Link zur Publikation
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Packungen aus Kreisscheiben
Autoren: Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly
(2019)
Wir beschäftigen uns mit Konfigurationen von gleichgroßen Kreisscheiben in einer Ebene, die sich nicht überlappen. Wir sind insbesondere daran interessiert, die Konfiguration(en) zu finden, die eine minimale quadratische Energie besitzen.
In der Tat, ist die genaue Geometrie der optimalen Konfiguration(en) nur für sehr kleine Systeme schon bekannt. Wir schlagen hier eine wahrscheinlichkeitstheoretische Methode vor, die effizient für Systeme jeder Größe ist.
Zeitschrift:
Elemente der Mathematik
2018 | Empilements de disques ou comment une approche probabiliste peut compléter une analyse géométrique ... | Charlotte Dombrowsky, Myriam Fradon, Sylvie RoellyZeitschrift: QuadratureBand: 107Link zur Publikation
Empilements de disques ou comment une approche probabiliste peut compléter une analyse géométrique ...
Autoren: Charlotte Dombrowsky, Myriam Fradon, Sylvie Roelly
(2018)
2017 | Algunas propiedades básicas de procesos de ramificación | S. RoellyReihe: Lectures in pure and applied mathematicsVerlag: Universitätsverlag PotsdamBuchtitel: Stochastic processes with applications in the natural sciences.international workshop at Universidad de los Andes, Bogotá, ColombiaSeiten: 29-79Band: 4Link zur Publikation
Algunas propiedades básicas de procesos de ramificación
Autoren: S. Roelly
(2017)
The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogotá, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics. The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume.
Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam.
Sylvie Rœlly, Docteur en Mathématiques, is the head of the chair of Probability at the University of Potsdam.
Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.
Reihe:
Lectures in pure and applied mathematics
Verlag:
Universitätsverlag Potsdam
Buchtitel:
Stochastic processes with applications in the natural sciences.international workshop at Universidad de los Andes, Bogotá, Colombia
2017 | Reciprocal class of jump processes | G. Conforti, P. dai Pra and S. RoellyZeitschrift: Journal of Theoretical ProbabilitySeiten: 551-580Band: 30-2Link zur Publikation
Reciprocal class of jump processes
Autoren: G. Conforti, P. dai Pra and S. Roelly
(2017)
Zeitschrift:
Journal of Theoretical Probability
2017 | Un destin singulier: Vincent, alias Wolfgang, fils d’Alfred Döblin | Sylvie RoellyZeitschrift: Dokumente/DocumentsBand: 4/2017Link zur Publikation
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Un destin singulier: Vincent, alias Wolfgang, fils d’Alfred Döblin
Autoren: Sylvie Roelly
(2017)
Un pli cacheté, envoyé par Wolfgang Döblin (1915-1940) à l’Académie des Sciences de Paris, mais ouvert seulement en 2000, met en évidence l’avant-gardisme du génie probabiliste du fils de l’écrivain Alfred Döblin (1878-1957), auteur notamment de Berlin, Alexanderplatz. Son inspiration mathématique géniale a puisé ses forces dans l’union des deux écoles française et allemande.
Zeitschrift:
Dokumente/Documents
2017 | Path-dependent infinite-dimensional SDE with non-regular drift: an existence result. | David Dereudre, Sylvie RoellyZeitschrift: Annales de l'Institut Henri Poincaré - Probabilités et StatistiquesSeiten: 641–657Band: 53 No.2Link zur Publikation
Path-dependent infinite-dimensional SDE with non-regular drift: an existence result.
Autoren: David Dereudre, Sylvie Roelly
(2017)
Zeitschrift:
Annales de l'Institut Henri Poincaré - Probabilités et Statistiques
2017 | Exact simulation of Brownian diffusions with drift admitting jumps | David Dereudre, Sara Mazzonetto, Sylvie RoellyZeitschrift: SIAM J. Sci. Comput., 39(3)Seiten: A711–A740Link zur Publikation
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Exact simulation of Brownian diffusions with drift admitting jumps
Autoren: David Dereudre, Sara Mazzonetto, Sylvie Roelly
(2017)
Zeitschrift:
SIAM J. Sci. Comput., 39(3)
2017 | Bridge mixtures of random walks on an Abelian group | G. Conforti and S. RoellyZeitschrift: BernoulliSeiten: 1518-1537Band: 23, No. 3Link zur Publikation
Bridge mixtures of random walks on an Abelian group
Autoren: G. Conforti and S. Roelly
(2017)
2016 | Convoluted Brownian motion | Sylvie Roelly, Pierre ValloisZeitschrift: Theory of Stochastic ProcessesReihe: 21 (37) no. 2Seiten: 58–83Link zur Publikation
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Convoluted Brownian motion
Autoren: Sylvie Roelly, Pierre Vallois
(2016)
Zeitschrift:
Theory of Stochastic Processes
2016 | Long time behavior of stochastic hard ball systems | P. Cattiaux, M. Fradon, A. Kulik, S. RoellyZeitschrift: Bernoulli 22-2 (2016)Seiten: 681-710Link zur Publikation
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Long time behavior of stochastic hard ball systems
Autoren: P. Cattiaux, M. Fradon, A. Kulik, S. Roelly
(2016)
Zeitschrift:
Bernoulli 22-2 (2016)
2016 | An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers | David Dereudre, Sara Mazzonetto, Sylvie RoellyZeitschrift: Monte Carlo Methods and Applications Vol. 22-1 (2016)Seiten: 1-23Link zur Publikation
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An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers
Autoren: David Dereudre, Sara Mazzonetto, Sylvie Roelly
(2016)
Zeitschrift:
Monte Carlo Methods and Applications Vol. 22-1 (2016)
2015 | On time duality for Markov chains | P. Keller, S. Roelly, A. VallerianiZeitschrift: Stochastic Models 31-1 (2015)Seiten: 98-118Link zur Publikation
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On time duality for Markov chains
Autoren: P. Keller, S. Roelly, A. Valleriani
(2015)
Zeitschrift:
Stochastic Models 31-1 (2015)
2015 | Bridges of Markov counting processes. Reciprocal classes and duality formulae | G. Conforti, C. Léonard, R. Murr, S. RoellyZeitschrift: Electron. Commun. Probab. 20-18 (2015)Seiten: 1-12Link zur Publikation
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Bridges of Markov counting processes. Reciprocal classes and duality formulae
Autoren: G. Conforti, C. Léonard, R. Murr, S. Roelly
(2015)
Zeitschrift:
Electron. Commun. Probab. 20-18 (2015)
2015 | A quasi Random Walk to model a biological transport process | P. Keller, S. Roelly, A. VallerianiZeitschrift: Methodology and Computing in Applied Probability 17 (2015)Seiten: 125-137Link zur Publikation
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A quasi Random Walk to model a biological transport process
Autoren: P. Keller, S. Roelly, A. Valleriani
(2015)
Zeitschrift:
Methodology and Computing in Applied Probability 17 (2015)
2014 | Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction | S. Roelly, W. RuszelZeitschrift: Markov Proc. Rel. FieldsSeiten: 653-674Band: 20Link zur Publikation
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Link zum Preprint
Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction
Autoren: S. Roelly, W. Ruszel
(2014)
Zeitschrift:
Markov Proc. Rel. Fields
2014 | Reciprocal processes: A measure-theoretical point of view | C. Léonard, S. Roelly, J.C. ZambriniZeitschrift: Probability SurveysSeiten: 237-269Band: 11Link zur Publikation
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Reciprocal processes: A measure-theoretical point of view
Autoren: C. Léonard, S. Roelly, J.C. Zambrini
(2014)
Zeitschrift:
Probability Surveys
2013 | Evolutive two-level population process and large population approximations | S. Méléard, S. RoellyZeitschrift: Ann. Univ. BucharestSeiten: 37-70Band: 4Link zur Publikation
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Evolutive two-level population process and large population approximations
Autoren: S. Méléard, S. Roelly
(2013)
Zeitschrift:
Ann. Univ. Bucharest
2013 | Reciprocal processes: a stochastic analysis approach | S. RoellyReihe: Springer Optimization and Its ApplicationsVerlag: SpringerBuchtitel: Modern Stochastics and ApplicationsSeiten: 53-67Band: 90Link zur Publikation
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Reciprocal processes: a stochastic analysis approach
Autoren: S. Roelly
(2013)
Reihe:
Springer Optimization and Its Applications
Buchtitel:
Modern Stochastics and Applications
2011 | Surveys in Stochastic Processes | S. Roelly (Ed.)Reihe: Series of Congress ReportsVerlag: EMSBuchtitel: Surveys in Stochastic ProcessesLink zur Publikation
Surveys in Stochastic Processes
Autoren: S. Roelly (Ed.)
(2011)
Reihe:
Series of Congress Reports
Buchtitel:
Surveys in Stochastic Processes
2010 | Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction | F. Redig, S. Roelly, W. RuszelZeitschrift: J. Stat. Phys.Seiten: 1124-1144"Band: 138Link zur Publikation
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Link zum Preprint
Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction
Autoren: F. Redig, S. Roelly, W. Ruszel
(2010)
Zeitschrift:
J. Stat. Phys.
2010 | Infinitely many Brownian globules with Brownian radii | M. Fradon, S. RoellyZeitschrift: Stoch. Dyn.Seiten: 591-612Band: 10Link zur Publikation
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Infinitely many Brownian globules with Brownian radii
Autoren: M. Fradon, S. Roelly
(2010)