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 = {Zt , 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 L2-continuity of the
semigroup {Tt , t ≥ 0 } given by Ttf(x)=
Ex[Zt f(Xt) ], 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