Letzte Publikationen

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 , Link zum Preprint

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
Band:
171

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 , Link zum Preprint

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
Seiten:
1497-1521
Band:
75 (11)

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
Seiten:
1-306

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 , Link zum Preprint

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
Seiten:
962-982
Band:
59 (4)

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 , Link zum Preprint

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
Seiten:
631-642
Band:
39 (4)

2020 | Marked Gibbs point processes with unbounded interaction: an existence result | Sylvie Roelly, Alexander ZassZeitschrift: Journal of Statistical PhysicsSeiten: 972–996Band: 179Link zur Publikation , Link zum Preprint

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
Seiten:
972–996
Band:
179

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
Band:
6

2020 | Pinned diffusions and Markov bridges | Florian Hildebrandt, Sylvie RoellyZeitschrift: Journal of Theoretical ProbabilitySeiten: 906-917Band: 33Link zur Publikation , Link zum Preprint

Pinned diffusions and Markov bridges

Autoren: Florian Hildebrandt, Sylvie Roelly (2020)

In this article we consider a family of real-valued di ffusion 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 di ffusion coefficients ensuring that the di ffusion is pinned in y at time 1. Our main result then concerns the following question: can this family of pinned diff usions be obtained as the bridges either of a Gaussian Markov process or of an Ito di ffusion? We eventually illustrate our precise answer with several examples.

Zeitschrift:
Journal of Theoretical Probability
Seiten:
906-917
Band:
33

2019 | Conditioned point processes with application to Lévy bridges | Giovanni Conforti, Tetiana Kosenkova, Sylvie RoellyZeitschrift: Journal of Theoretical ProbabilitySeiten: 2111-2134Band: 32Link zur Publikation , Link zum Preprint

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
Seiten:
2111-2134
Band:
32

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
Reihe:
Les 80 ans du CNRS
Verlag:
Institut Henri Poincaré

2019 | Packungen aus Kreisscheiben | Charlotte Dombrowsky, Myriam Fradon, Sylvie RoellyZeitschrift: Elemente der MathematikSeiten: pp.45-62Band: 74-2Link zur Publikation , Link zum Preprint

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
Seiten:
pp.45-62
Band:
74-2

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)

Zeitschrift:
Quadrature
Band:
107

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
Seiten:
29-79
Band:
4

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
Seiten:
551-580
Band:
30-2

2017 | Un destin singulier: Vincent, alias Wolfgang, fils d’Alfred Döblin | Sylvie RoellyZeitschrift: Dokumente/DocumentsBand: 4/2017Link zur Publikation , Link zum Preprint

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
Band:
4/2017

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
Seiten:
641–657
Band:
53 No.2

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 , Link zum Preprint

Exact simulation of Brownian diffusions with drift admitting jumps

Autoren: David Dereudre, Sara Mazzonetto, Sylvie Roelly (2017)

Zeitschrift:
SIAM J. Sci. Comput., 39(3)
Seiten:
A711–A740

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)

Zeitschrift:
Bernoulli
Seiten:
1518-1537
Band:
23, No. 3

2016 | Convoluted Brownian motion | Sylvie Roelly, Pierre ValloisZeitschrift: Theory of Stochastic ProcessesReihe: 21 (37) no. 2Seiten: 58–83Link zur Publikation , Link zum Preprint

Convoluted Brownian motion

Autoren: Sylvie Roelly, Pierre Vallois (2016)

Zeitschrift:
Theory of Stochastic Processes
Reihe:
21 (37) no. 2
Seiten:
58–83

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 , Link zum Preprint

Long time behavior of stochastic hard ball systems

Autoren: P. Cattiaux, M. Fradon, A. Kulik, S. Roelly (2016)

Zeitschrift:
Bernoulli 22-2 (2016)
Seiten:
681-710

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 , Link zum Preprint

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)
Seiten:
1-23

2015 | On time duality for Markov chains | P. Keller, S. Roelly, A. VallerianiZeitschrift: Stochastic Models 31-1 (2015)Seiten: 98-118Link zur Publikation , Link zum Preprint

On time duality for Markov chains

Autoren: P. Keller, S. Roelly, A. Valleriani (2015)

Zeitschrift:
Stochastic Models 31-1 (2015)
Seiten:
98-118

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 , Link zum Preprint

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)
Seiten:
1-12

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 , Link zum Preprint

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)
Seiten:
125-137

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 , 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
Seiten:
653-674
Band:
20

2014 | Reciprocal processes: A measure-theoretical point of view | C. Léonard, S. Roelly, J.C. ZambriniZeitschrift: Probability SurveysSeiten: 237-269Band: 11Link zur Publikation , Link zum Preprint

Reciprocal processes: A measure-theoretical point of view

Autoren: C. Léonard, S. Roelly, J.C. Zambrini (2014)

Zeitschrift:
Probability Surveys
Seiten:
237-269
Band:
11

2013 | Evolutive two-level population process and large population approximations | S. Méléard, S. RoellyZeitschrift: Ann. Univ. BucharestSeiten: 37-70Band: 4Link zur Publikation , Link zum Preprint

Evolutive two-level population process and large population approximations

Autoren: S. Méléard, S. Roelly (2013)

Zeitschrift:
Ann. Univ. Bucharest
Seiten:
37-70
Band:
4

2013 | Reciprocal processes: a stochastic analysis approach | S. RoellyReihe: Springer Optimization and Its ApplicationsVerlag: SpringerBuchtitel: Modern Stochastics and ApplicationsSeiten: 53-67Band: 90Link zur Publikation , Link zum Preprint

Reciprocal processes: a stochastic analysis approach

Autoren: S. Roelly (2013)

Reihe:
Springer Optimization and Its Applications
Verlag:
Springer
Buchtitel:
Modern Stochastics and Applications
Seiten:
53-67
Band:
90

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
Verlag:
EMS
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 , 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.
Seiten:
1124-1144"
Band:
138

2010 | Infinitely many Brownian globules with Brownian radii | M. Fradon, S. RoellyZeitschrift: Stoch. Dyn.Seiten: 591-612Band: 10Link zur Publikation , Link zum Preprint

Infinitely many Brownian globules with Brownian radii

Autoren: M. Fradon, S. Roelly (2010)

Zeitschrift:
Stoch. Dyn.
Seiten:
591-612
Band:
10