Gibbs measures with double stochastic integrals on a path space

Volkerr Betz; Fumio Hiroshima

doi:10.1142/S0219025709003574

Gibbs measures with double stochastic integrals on a path space

Volkerr Betz
, Fumio Hiroshima

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the PauliFierz model in nonrelativistic quantum electrodynamics, we prove the existence of its infinite volume limit.

Original language	English
Pages (from-to)	135-152
Number of pages	18
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	12
Issue number	1
DOIs	https://doi.org/10.1142/S0219025709003574
Publication status	Published - Mar 2009

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

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title = "Gibbs measures with double stochastic integrals on a path space",

abstract = "We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the PauliFierz model in nonrelativistic quantum electrodynamics, we prove the existence of its infinite volume limit.",

keywords = "Double stochastic integral, Gibbs measures, Pauli-Fierz model",

author = "Volkerr Betz and Fumio Hiroshima",

note = "Funding Information: V.B. wishes to thank the University of Kyushu, Japan, where the present work was started, for kind hospitality. F.H. wishes to thank the University of Warwick in UK, where this work was partially done, for kind hospitality. V.B. was supported by an EPSRC fellowship EP/D07181X/1. F.H. was supported by Grant-in-Aid for Science Research (C) 17540181 and (B) 20340032 from JSPS.",

year = "2009",

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T1 - Gibbs measures with double stochastic integrals on a path space

AU - Betz, Volkerr

AU - Hiroshima, Fumio

N1 - Funding Information: V.B. wishes to thank the University of Kyushu, Japan, where the present work was started, for kind hospitality. F.H. wishes to thank the University of Warwick in UK, where this work was partially done, for kind hospitality. V.B. was supported by an EPSRC fellowship EP/D07181X/1. F.H. was supported by Grant-in-Aid for Science Research (C) 17540181 and (B) 20340032 from JSPS.

PY - 2009/3

Y1 - 2009/3

N2 - We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the PauliFierz model in nonrelativistic quantum electrodynamics, we prove the existence of its infinite volume limit.

AB - We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the PauliFierz model in nonrelativistic quantum electrodynamics, we prove the existence of its infinite volume limit.

KW - Double stochastic integral

KW - Gibbs measures

KW - Pauli-Fierz model

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JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

IS - 1

ER -

Gibbs measures with double stochastic integrals on a path space

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