@unpublished{Roelly2010,
  author    = {Roelly, Sylvie},
  title     = {Unas propiedades basicas de procesos de ramificaci{\´o}n : Lectures held at ICIMAF La Habana, Cuba, 2009 and 2010},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49620},
  year      = {2010},
  abstract  = {Aus dem Inhalt: 1. Unas propiedades de los procesos de Bienaym{\´e}-Galton-Watson de tiempo dis- creto (BGW) 2. Unas propiedades del proceso BGW de tiempo continuo 3. Limites de procesos de BGW cuando la poblaci{\´o}n es numerosa},
  language  = {mul}
}
@unpublished{LeonardRoellyZambrini2013,
  author    = {L{\´e}onard, Christian and Roelly, Sylvie and Zambrini, Jean-Claude},
  title     = {Temporal symmetry of some classes of stochastic processes},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64599},
  year      = {2013},
  abstract  = {In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.},
  language  = {en}
}
@inproceedings{VallerianiRoellyKulik2017,
  author    = {Valleriani, Angelo and Roelly, Sylvie and Kulik, Alexei Michajlovič},
  title     = {Stochastic processes with applications in the natural sciences},
  series = {Lectures in pure and applied mathematics},
  booktitle = {Lectures in pure and applied mathematics},
  number    = {4},
  editor    = {Roelly, Sylvie and H{\"o}gele, Michael and Rafler, Mathias},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-414-2},
  issn      = {2199-4951},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-401802},
  pages     = {ix, 124},
  year      = {2017},
  abstract  = {The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogot{\´a}, 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 Math{\´e}matiques, 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.},
  language  = {en}
}
@misc{RoellySortais2004,
  author    = {Roelly, Sylvie and Sortais, Michel},
  title     = {Space-time asymptotics of an infinite-dimensional diffusion having a long- range memory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-6700},
  year      = {2004},
  abstract  = {We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field.},
  language  = {en}
}
@unpublished{RedigRoellyRuszel2009,
  author    = {Redig, Frank and Roelly, Sylvie and Ruszel, Wioletta},
  title     = {Short-time Gibbsianness for infinite-dimensional diffusions with space-time interaction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49514},
  year      = {2009},
  abstract  = {We consider a class of infinite-dimensional diffusions where the interaction between the components is both spatial and temporal. We start the system from a Gibbs measure with finiterange uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t0 > 0 such that the distribution at time t = t0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.},
  language  = {de}
}
@unpublished{Roelly2013,
  author    = {Roelly, Sylvie},
  title     = {Reciprocal processes : a stochastic analysis approach},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64588},
  year      = {2013},
  abstract  = {Reciprocal processes, whose concept can be traced back to E. Schr{\"o}dinger, form a class of stochastic processes constructed as mixture of bridges, that satisfy a time Markov field property. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This presentation is based on joint works with M. Thieullen, R. Murr and C. L{\´e}onard.},
  language  = {en}
}
@unpublished{ConfortiRoelly2015,
  author    = {Conforti, Giovanni and Roelly, Sylvie},
  title     = {Reciprocal class of random walks on an Abelian group},
  volume    = {4},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72604},
  pages     = {22},
  year      = {2015},
  abstract  = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.},
  language  = {en}
}
@article{ConfortiPraRoelly2015,
  author    = {Conforti, Giovanni and Pra, Paolo Dai and Roelly, Sylvie},
  title     = {Reciprocal Class of Jump Processes},
  series = {Journal of theoretical probability},
  volume    = {30},
  journal   = {Journal of theoretical probability},
  publisher = {Springer},
  address   = {New York},
  issn      = {0894-9840},
  doi       = {10.1007/s10959-015-0655-3},
  pages     = {551 -- 580},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@unpublished{ConfortiDaiPraRoelly2014,
  author    = {Conforti, Giovanni and Dai Pra, Paolo and Roelly, Sylvie},
  title     = {Reciprocal class of jump processes},
  volume    = {3},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70776},
  pages     = {30},
  year      = {2014},
  abstract  = {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 A in R^d. 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 A 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.},
  language  = {en}
}
@unpublished{DereudreRoelly2004,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {Propagation of Gibbsianness for infinite-dimensional gradient Brownian diffusions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51535},
  year      = {2004},
  abstract  = {We study the (strong-)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion , when the initial distribution is Gibbsian.},
  language  = {en}
}
@article{RoellyRuszel2014,
  author    = {Roelly, Sylvie and Ruszel, W. M.},
  title     = {Propagation of gibbsianness for infinite-dimensional diffusions with space-time interaction},
  series = {Markov processes and related fields},
  volume    = {20},
  journal   = {Markov processes and related fields},
  number    = {4},
  publisher = {Polymat},
  address   = {Moscow},
  issn      = {1024-2953},
  pages     = {653 -- 674},
  year      = {2014},
  abstract  = {We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.},
  language  = {en}
}
@unpublished{RoellyRuszel2013,
  author    = {Roelly, Sylvie and Ruszel, Wioletta M.},
  title     = {Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69014},
  year      = {2013},
  abstract  = {We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.},
  language  = {en}
}
@misc{RoellyDereudre2004,
  author    = {Roelly, Sylvie and Dereudre, David},
  title     = {Propagation of Gibbsiannes for infinite-dimensional gradient Brownian diffusions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-6918},
  year      = {2004},
  abstract  = {We study the (strong-)Gibbsian character on R Z d of the law at time t of an infinitedimensional gradient Brownian diffusion , when the initial distribution is Gibbsian.},
  language  = {en}
}
@unpublished{DereudreRoelly2014,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {Path-dependent infinite-dimensional SDE with non-regular drift : an existence result},
  volume    = {3},
  number    = {11},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72084},
  pages     = {27},
  year      = {2014},
  abstract  = {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 small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.},
  language  = {en}
}
@article{DereudreRoelly2017,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {Path-dependent infinite-dimensional SDE with non-regular drift},
  series = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics},
  volume    = {53},
  journal   = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics},
  number    = {2},
  publisher = {Inst. of Mathematical Statistics},
  address   = {Bethesda},
  issn      = {0246-0203},
  doi       = {10.1214/15-AIHP728},
  pages     = {641 -- 657},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{DombrowskyUndRoelly2019,
  author    = {Dombrowsky, Charlotte and Und, Myriam Fradon and Roelly, Sylvie},
  title     = {Packungen aus Kreisscheiben},
  series = {Elemente der Mathematik},
  volume    = {74},
  journal   = {Elemente der Mathematik},
  number    = {2},
  publisher = {EMS Publ.},
  address   = {Z{\"u}rich},
  issn      = {0013-6018},
  doi       = {10.4171/EM/381},
  pages     = {45 -- 62},
  year      = {2019},
  abstract  = {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 N{\"a}herungen der L{\"o}sung zu konstruieren.},
  language  = {de}
}
@unpublished{KellerRoellyValleriani2012,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {On time duality for quasi-birth-and-death processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56973},
  year      = {2012},
  abstract  = {We say that (weak/strong) time duality holds for continuous time quasi-birth-and-death-processes if, starting from a fixed level, the first hitting time of the next upper level and the first hitting time of the next lower level have the same distribution. We present here a criterion for time duality in the case where transitions from one level to another have to pass through a given single state, the so-called bottleneck property. We also prove that a weaker form of reversibility called balanced under permutation is sufficient for the time duality to hold. We then discuss the general case.},
  language  = {en}
}
@book{KellerRoellyValleriana2011,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriana, Angelo},
  title     = {On Time Duality for Markov Chains with Asborbing Boundardies},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1613-3307},
  pages     = {18 S.},
  year      = {2011},
  language  = {en}
}
@article{KellerRoellyValleriani2015,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {On time duality for Markov Chains},
  series = {Stochastic models},
  volume    = {31},
  journal   = {Stochastic models},
  number    = {1},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {1532-6349},
  doi       = {10.1080/15326349.2014.969736},
  pages     = {98 -- 118},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@book{DereudreRoelly2004,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {On Gibbsianness of infinite-dimensional diffussions},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Mathematische Statistik un},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1613-3307},
  pages     = {14 S.},
  year      = {2004},
  language  = {en}
}