On general perturbations of symmetric Markov processes
On general perturbations of symmetric Markov processes
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DOI：
10.1016/j.matpur.2009.05.012
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
Zhen-Qing Chen;P. Fitzsimmons;K. Kuwae;Tusheng Zhang
中科院分区：
文献类型：
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作者：
Zhen-Qing Chen;P. Fitzsimmons;K. Kuwae;Tusheng Zhang
设X是一个对称右过程，Z={Zt，t <$0}是X的一个乘法泛函，它是一个Girsanov变换、一个时间反演下的Girsanov变换和一个连续Feynman-Kac变换的乘积.本文给出了由Ttf（x）=Ex[Ztf（Xt）]给出的半群{Tt，t <$0}的强L2连续的充要条件，这些条件用扰动X的Dirichlet型得到的二次型表示.这种Z引起的变换包括所有以前在文献中处理过的变换，如Girsanov变换，连续和不连续Feynman-Kac变换，以及广义Feynman-Kac变换。
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[Ztf(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.