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.

**[1]**R. M. Blumenthal and R. K. Getoor,*Markov processes and potential theory*, Academic Press, New York, 1968. MR**0264757 (41:9348)****[2]**K. L. Chung,*Lectures from Markov processes to Brownian motion*, Springer-Verlag, Berlin and New York, 1985. MR**648601 (84c:60091)****[3]**-,*Doubly Feller process with multiplicative functional*, Seminar on Stochastic Processes, Birkhauser, 1985, pp. 63-78. MR**896735 (88k:60128)****[4]**-,*Properties of finite gauge with an application to local time*, Essays in honor of Carl-Gustav Esseen, Uppsala, Sweden, 1983, pp. 16-24. MR**727123 (85d:60142)****[5]**-,*Notes on the inhomogeneous Schrödinger equation*, Seminar on Stochastic Processes, Birkhäuser, 1984, pp. 55-62. MR**896721 (89h:60136)****[6]**K. L. Chung and Z. Zhao, forthcoming monograph.**[7]**K. L. Chung and M. Rao,*A new setting for potential theory*, Ann. Inst. Fourier (Grenoble)**30**(1980), 167-198. MR**597022 (82k:60150a)****[8]**-,*Feynman-Kac functional and the Schrödinger equation*, Seminar on Stochastic Processes, Birkhäuser, 1981, pp. 1-29. MR**647779 (83g:60089)****[9]**C. Dellacheri and P. A. Meyer,*Probabilités et potentiel*, Hermann, Paris, 1980. MR**0488194 (58:7757)****[10]**D. Revuz,*Mesures associees aux fonctionelles additives de Markov*. I, Trans. Amer. Math. Soc.**148**(1970), 501-531. MR**0279890 (43:5611)**

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

Article copyright:
© Copyright 1988
American Mathematical Society