Conditional gauge theorem for non-local Feynman-Kac transforms

Zhen Qing Chen; Renming Song

doi:10.1007/s004400200219

Conditional gauge theorem for non-local Feynman-Kac transforms

Zhen Qing Chen^*
, Renming Song

^*Corresponding author for this work

University of Washington
University of Illinois at Urbana-Champaign

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

44 Citations (Scopus)

Abstract

Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L²-infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.

Original language	English
Pages (from-to)	45-72
Number of pages	28
Journal	Probability Theory and Related Fields
Volume	125
Issue number	1
DOIs	https://doi.org/10.1007/s004400200219
Publication status	Published - Jan 2003
Externally published	Yes

Keywords

Conditional Markov process
Conditional gauge theorem
Gauge Theorem
Green function
Kato class

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10.1007/s004400200219

Cite this

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title = "Conditional gauge theorem for non-local Feynman-Kac transforms",

abstract = "Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L2-infinitesimal generator of the Schr{\"o}dinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.",

keywords = "Conditional Markov process, Conditional gauge theorem, Gauge Theorem, Green function, Kato class",

author = "Chen, \{Zhen Qing\} and Renming Song",

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AU - Chen, Zhen Qing

AU - Song, Renming

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N2 - Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L2-infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.

AB - Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L2-infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.

KW - Conditional Markov process

KW - Conditional gauge theorem

KW - Gauge Theorem

KW - Green function

KW - Kato class

UR - https://www.scopus.com/pages/publications/0037934617

U2 - 10.1007/s004400200219

DO - 10.1007/s004400200219

M3 - Article

AN - SCOPUS:0037934617

SN - 0178-8051

VL - 125

SP - 45

EP - 72

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1

ER -

Conditional gauge theorem for non-local Feynman-Kac transforms

Abstract

Keywords

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