On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems

da Silva J, Kondratiev Y, Röckner M (2001)
MATHEMATISCHE NACHRICHTEN 222: 141-157.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
In this paper we extend the result obtained in [AKR98] (see also [AKR96a]) on the representation of the intrinsic pre-Dirichlet form epsilon (Gamma)(pi sigma) of the Poisson measure pi (sigma) in terms of the extrinsic one epsilon (P)(pi sigma ,H sigmaX). More precisely, replacing pi (sigma) by a Gibbs measure mu on the configuration space Gamma (X) we derive a relation between the intrinsic pre-Dirichlet form epsilon (Gamma)(mu) of the measure mu and the extrinsic epsilon (P)(mu ,H sigmaX). As a consequence we prove the closability of epsilon (Gamma)(mu) on L-2(Gamma (X), mu) under very general assumptions on the interaction potential of the Gibbs measures mu.
Erscheinungsjahr
Zeitschriftentitel
MATHEMATISCHE NACHRICHTEN
Band
222
Seite(n)
141-157
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da Silva J, Kondratiev Y, Röckner M. On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems. MATHEMATISCHE NACHRICHTEN. 2001;222:141-157.
da Silva, J., Kondratiev, Y., & Röckner, M. (2001). On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems. MATHEMATISCHE NACHRICHTEN, 222, 141-157. doi:10.1002/1522-2616(200102)222:1<141::AID-MANA141>3.0.CO;2-M
da Silva, J., Kondratiev, Y., and Röckner, M. (2001). On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems. MATHEMATISCHE NACHRICHTEN 222, 141-157.
da Silva, J., Kondratiev, Y., & Röckner, M., 2001. On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems. MATHEMATISCHE NACHRICHTEN, 222, p 141-157.
J. da Silva, Y. Kondratiev, and M. Röckner, “On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems”, MATHEMATISCHE NACHRICHTEN, vol. 222, 2001, pp. 141-157.
da Silva, J., Kondratiev, Y., Röckner, M.: On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems. MATHEMATISCHE NACHRICHTEN. 222, 141-157 (2001).
da Silva, José, Kondratiev, Yuri, and Röckner, Michael. “On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems”. MATHEMATISCHE NACHRICHTEN 222 (2001): 141-157.