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Theory of Probability and Mathematical Statistics

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Stochastic analysis with the gamma measure--Moving a dense set

Author: D. Hagedorn
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 149-158
MSC (2010): Primary 60G57, 28C20; Secondary 46G12, 58B20, 58J65, 60G55
Published electronically: January 14, 2013
MathSciNet review: 2933710
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Abstract: The Gamma measure corresponds to a measure on a marked configuration space with an infinite measure on the marks. We construct Dirichlet forms for the movement of marks and positions. These include the movement of the support, which is a dense set in $ \mathbb{R}^d$, $ d \in \mathbb{N}$. The key ingredient is a recently discovered integration by parts formula for the directional derivative w.r.t. the positions. We briefly introduce the geometry and then concentrate on the construction of the Dirichlet forms.

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  • 1. S. Albeverio, Yu. G. Kondratiev, and M. Röckner, Analysis and geometry on configuration spaces, Journal of Functional Analysis 154 (1998), no. 2, 444-500. MR 1612725 (99d:58179)
  • 2. M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics, vol. 19, de Gruyter, 1994. MR 1303354 (96f:60126)
  • 3. D. Hagedorn, Stochastic Analysis Related to Gamma Measures, Dissertation, Universität Bielefeld, 2011.
  • 4. D. Hagedorn, Yu. G. Kondratiev, and A. M. Vershik, Integration by Parts Formula for the Gamma Process, Preprint, Universität Bielefeld, 2010.
  • 5. Yu. Kondratiev, E. Lytvynov, and G. Us, Analysis and geometry on $ \mathbb{R}_+$-marked configuration space, Meth. Funct. Anal. Topol. 5 (1999), no. 1, 29-64. MR 1771250 (2001i:58075)
  • 6. Z.-M. Ma and M. Röckner, Introduction to the Theory of (Non-symmetric) Dirichlet Forms, Springer, 1992. MR 1214375 (94d:60119)
  • 7. N. Tsilevich, A. Vershik, and M. Yor, An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the Gamma process, Journal of Functional Analysis 185 (2001), no. 1, 274-296. MR 1853759 (2002g:46071)
  • 8. A. M. Veršik, I. M. Gel'fand, and M. I. Graev, Representations of the group of diffeomorphisms, Uspehi Mat. Nauk 30 (1975), no. 6(186), 1-50. MR 0399343 (53:3188)

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Additional Information

D. Hagedorn
Affiliation: Fakultät für Mathematik, Universität Bielefeld, D-33615 Bielefeld, Germany

Received by editor(s): April 15, 2011
Published electronically: January 14, 2013
Additional Notes: The author thanks Professor Yuri Kondratiev and Professor Anatoly Vershik for useful discussions and valuable comments. Support through the International Graduate College 1132 “Stochastics and Real World Models” and the SFB-701 is gratefully acknowledged
The paper is based on the talk presented at the International Conference “Modern Stochastics: Theory and Applications II” held on September 7–11, 2010, at Kyiv National Taras Shevchenko University and dedicated to the anniversaries of three prominent Ukrainian scientists: Anatolii Skorokhod, Volodymyr Korolyuk and Igor Kovalenko
Article copyright: © Copyright 2013 American Mathematical Society

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