@article{ConfortiLeonardMurretal.2015,
  author    = {Conforti, Giovanni and Leonard, Christian and Murr, R{\"u}diger and Roelly, Sylvie},
  title     = {Bridges of Markov counting processes. Reciprocal classes and duality formulas},
  series = {Electronic communications in probability},
  volume    = {20},
  journal   = {Electronic communications in probability},
  publisher = {Univ. of Washington, Mathematics Dep.},
  address   = {Seattle},
  issn      = {1083-589X},
  doi       = {10.1214/ECP.v20-3697},
  pages     = {12},
  year      = {2015},
  abstract  = {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.},
  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@unpublished{ConfortiRoelly2015,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}
}
@unpublished{DereudreMazzonettoRoelly2015,
  author    = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie},
  title     = {An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers},
  volume    = {4},
  number    = {9},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-80613},
  pages     = {23},
  year      = {2015},
  abstract  = {In this paper we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover we propose a rejection method to simulate this density in an exact way.},
  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}
}
@article{KellerRoellyValleriani2015,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {A Quasi Random Walk to Model a Biological Transport Process},
  series = {Methodology and computing in applied probability},
  volume    = {17},
  journal   = {Methodology and computing in applied probability},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1387-5841},
  doi       = {10.1007/s11009-013-9372-5},
  pages     = {125 -- 137},
  year      = {2015},
  abstract  = {Transport molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance and requires several biochemical transformations, which are modeled as internal states of the motor. While moving along the rope, the motor can also detach and the walk is interrupted. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.},
  language  = {en}
}