excmin
### On General Perturbations of Symmetric Markov Processes

#### Z.-Q. Chen, P.J. Fitzsimmons, K. Kuwae, T.-S. Zhang

Let *X* be a symmetric right process, and let *Z* = {*Z*_{t} , *t* ≥ 0}
be a multiplicative functional of *X* that is the product of a
Girsanov transform, a Girsanov transform under time-reversal and a
continuous Feynman-Kac transform. In this paper we derive necessary
and sufficient conditions for the strong *L*^{2}-continuity of the
semigroup {*T*_{t} , t ≥ 0 } given by *T*_{t}f(x)=
**E**_{x}[*Z*_{t} f(X_{t}) ], expressed in terms of the quadratic form obtained
by perturbing the Dirichlet form of *X* in the appropriate way.
The transformations induced by such *Z* include all those treated previously
in the literature, such as Girsanov transforms, continuous
and discontinuous Feynman-Kac transforms, and generalized Feynman-Kac
transforms.

This manuscript is available from the first-named author upon request.

The manuscript can also be downloaded
as a pdf file (224K).

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November 12, 2008