@unpublished{Murr2008,
  author    = {Murr, R{\"u}diger},
  title     = {Dualit{\"a}tsformeln f{\"u}r Brownsche Bewegung und f{\"u}r eine Irrfahrt mit Anwendung am Konvergenzergebnis von Donsker},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49476},
  year      = {2008},
  abstract  = {Aus dem Inhalt: 0.1 Danksagung 0.2 Einleitung 1 Allgemeines und Grundlagen 1.1 Die Brownsche Bewegung 2 Die Dualit{\"a}tsformel des Wienermaßes 2.1 Wienermaß erf{\"u}llt Dualit{\"a}tsformel 2.2 Dualit{\"a}tsformel charakterisiert Wienermaß 3 Die diskrete Dualit{\"a}tsformel der Irrfahrt 3.1 Verallgemeinerte symmetrische Irrfahrt erf{\"u}llt diskrete Dualit{\"a}tsformel 3.2 Diskrete Dualit{\"a}tsformel charakterisiert verallgemeinerte symmetrische Irrfahrt 4 Donskers Theorem und die Dualit{\"a}tsformeln 4.1 Straffheit der renormierten stetigen Irrfahrt 4.2 Konvergenz der Irrfahrt 5 Anhang},
  language  = {de}
}
@unpublished{Murr2011,
  author    = {Murr, R{\"u}diger},
  title     = {Characterization of L{\´e}vy Processes by a duality formula and related results},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-43538},
  year      = {2011},
  abstract  = {Processes with independent increments are characterized via a duality formula, including Malliavin derivative and difference operators. This result is based on a characterization of infinitely divisible random vectors by a functional equation. A construction of the difference operator by a variational method is introduced and compared to approaches used by other authors for L´evy processes involving the chaos decomposition. Finally we extend our method to characterize infinitely divisible random measures.},
  language  = {en}
}
@unpublished{Murr2012,
  author    = {Murr, R{\"u}diger},
  title     = {Reciprocal classes of Markov processes : an approach with duality formulae},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63018},
  year      = {2012},
  abstract  = {In this work we are concerned with the characterization of certain classes of stochastic processes via duality formulae. First, we introduce a new formulation of a characterization of processes with independent increments, which is based on an integration by parts formula satisfied by infinitely divisible random vectors. Then we focus on the study of the reciprocal classes of Markov processes. These classes contain all stochastic processes having the same bridges, and thus similar dynamics, as a reference Markov process. We start with a resume of some existing results concerning the reciprocal classes of Brownian diffusions as solutions of duality formulae. As a new contribution, we show that the duality formula satisfied by elements of the reciprocal class of a Brownian diffusion has a physical interpretation as a stochastic Newton equation of motion. In the context of pure jump processes we derive the following new results. We will analyze the reciprocal classes of Markov counting processes and characterize them as a group of stochastic processes satisfying a duality formula. This result is applied to time-reversal of counting processes. We are able to extend some of these results to pure jump processes with different jump-sizes, in particular we are able to compare the reciprocal classes of Markov pure jump processes through a functional equation between the jump-intensities.},
  language  = {en}
}
@unpublished{ConfortiLeonardMurretal.2014,
  author    = {Conforti, Giovanni and L{\´e}onard, Christian and Murr, R{\"u}diger and Roelly, Sylvie},
  title     = {Bridges of Markov counting processes : reciprocal classes and duality formulas},
  volume    = {3},
  number    = {9},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71855},
  pages     = {12},
  year      = {2014},
  abstract  = {Processes having 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}
}