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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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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DOI: https://doi.org/10.1007/s004400200219
Keywords
- Markov Process
- Large Class
- Bilinear Form
- General Gauge
- Additive Functional