Stochastic analysis related to Gamma measures [Elektronische Ressource] : Gibbs perturbations and associated diffusions / Dennis Hagedorn. Fakultät für Mathematik

ThesisStochastic Analysis related to Gammameasures- Gibbs perturbations and associated DiffusionsDissertationzurErlangung des Doktorgrades (Dr. math.)derFakultät für MathematikderUniversität Bielefeldvorgelegt vonDennis Hagedorn aus Minden (Westf.)imNovember 2011iiIm Zuge der Veröffentlichung wurde die vorliegende Dissertation redaktionellkorrigiert.Bielefeld, im Dezember 2011iiiSummaryIn this thesis (consisting of Parts I - III) we study Gamma measures located on thedcone (R ) of discrete Radon measures. They form, as well as the Gaussian andPoisson measures, an important class of measures on infinite dimensional spacesand appeared in the representation theory of groups. In the present thesis, thefollowing topics of Gamma analysis are developed: Construction of Gibbs perturbations for the Gamma measuresd Differential structure on the cone (R ) Integration by parts formulas for Gamma and Gibbs measures Construction of associated diffusionsdIn Part I, we define a homeomorphism between the cone (R ) and a subsetd d^ ^of the configuration space ( R ) over the product space R of marks in R :=+d(0;1) and positions in R . This subset consists of pinpointing configurationsdwith finite local mass. Then we construct Gamma measures on (R ) as imaged^measures, under , of proper Poisson measures on ( R ).In Part II, we establish Gibbs perturbations of Gamma measures w.r.t.