General gauge theorem for multiplicative functionals

Authors:
K. L. Chung and K. M. Rao

Journal:
Trans. Amer. Math. Soc. **306** (1988), 819-836

MSC:
Primary 60J40; Secondary 60J57

DOI:
https://doi.org/10.1090/S0002-9947-1988-0933320-1

MathSciNet review:
933320

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Abstract: We generalize our previous work on the gauge theorem and its various consequences and complements, initiated in [**8**] and somewhat extended by subsequent investigations (see [**6**]). The generalization here is two-fold. First, instead of the Brownian motion, the underlying process is now a fairly broad class of Markov processes, not necessarily having continuous paths. Second, instead of the Feynman-Kac functional, the exponential of a general class of additive functionals is treated. The case of Schrödinger operator , where is a suitable measure, is a simple special case. The most general operator, not necessarily a differential one, which may arise from our potential equations is briefly discussed toward the end of the paper. Concrete instances of applications in this case should be of great interest.

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DOI:
https://doi.org/10.1090/S0002-9947-1988-0933320-1

Article copyright:
© Copyright 1988
American Mathematical Society