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Conditional gauge theorem for non-local Feynman-Kac transforms
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  • Published: January 2003

Conditional gauge theorem for non-local Feynman-Kac transforms

  • Zhen-Qing Chen1 &
  • Renming Song2 

Probability Theory and Related Fields volume 125, pages 45–72 (2003)Cite this article

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  • 40 Citations

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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 L 2-infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA 98195, USA. e-mail: zchen@math.washington.edu, , , , , , US

    Zhen-Qing Chen

  2. Department of Mathematics, University of Illinois, Urbana, IL 61801, USA. e-mail: rsong@math.uiuc.edu, , , , , , US

    Renming Song

Authors
  1. Zhen-Qing Chen
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  2. Renming Song
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Additional information

Received: 3 July 2001 / Revised version: 10 January 2002 / Published online: 10 September 2002

The research of this author is supported in part by NSF Grant DMS-9803240

Mathematics Subject Classification (2000): Primary 60J45, 60J40; Secondary 35J10, 47J20

Key words or phrases: Green function – Conditional Markov process – Kato class – Conditional gauge theorem – Gauge Theorem

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Chen, ZQ., Song, R. Conditional gauge theorem for non-local Feynman-Kac transforms. Probab Theory Relat Fields 125, 45–72 (2003). https://doi.org/10.1007/s004400200219

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  • Issue Date: January 2003

  • DOI: https://doi.org/10.1007/s004400200219

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Keywords

  • Markov Process
  • Large Class
  • Bilinear Form
  • General Gauge
  • Additive Functional
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