Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces

Albeverio S, Kondratiev Y, Röckner M (1996)
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 323(11): 1179-1184.

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Zeitschriftenaufsatz | Veröffentlicht | Französisch
Abstract / Bemerkung
We derive the precise relation of the internal differential geometry of Poisson spaces developed in [1] to the corresponding external geometry given by the associated Fock structure. In particular, we identify the (internal) Laplace-Beltrami operator H-pi sigma(Gamma) on Poisson space as the second quantization of the Laplacian on R(d). Furthermore, the diffusion process generated by H-pi sigma(Gamma), which is a kind of distorted Brownian motion on the configuration space, is described explicitly. All this generalizes to the case where the underlying Euclidean space R(d) is replaced by an (infinite-dimensional) manifold.
Erscheinungsjahr
Zeitschriftentitel
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
Band
323
Ausgabe
11
Seite(n)
1179-1184
ISSN
PUB-ID

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Albeverio S, Kondratiev Y, Röckner M. Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE. 1996;323(11):1179-1184.
Albeverio, S., Kondratiev, Y., & Röckner, M. (1996). Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 323(11), 1179-1184.
Albeverio, S., Kondratiev, Y., and Röckner, M. (1996). Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 323, 1179-1184.
Albeverio, S., Kondratiev, Y., & Röckner, M., 1996. Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 323(11), p 1179-1184.
S. Albeverio, Y. Kondratiev, and M. Röckner, “Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces”, COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, vol. 323, 1996, pp. 1179-1184.
Albeverio, S., Kondratiev, Y., Röckner, M.: Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE. 323, 1179-1184 (1996).
Albeverio, Sergio, Kondratiev, Yuri, and Röckner, Michael. “Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces”. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 323.11 (1996): 1179-1184.