关于广义Feynman-Kac半群的一个注记

A note of generalized Feynman-Kac semigroups

设(Xt)t>0是Lévy过程,(ε,D(ε))为其联系的狄氏型;对任意的u∈D(ε),设Ntu为u(Xt)-u(X0)的Fukushima分解中的零能量连续可加泛函.本论文主要研究了广义Feynman-Kac半群Ttf(x)=Ex[ef(Xt)],得到当u的能量测度μ<u>属于Hardy类且Hardy类系数大于0小于12时,(Tt)t≥0是强连续半群,并且得到了其对应的二次型表达式.

Let x be a Lévy process and （ε,D （ε）） be the Dirichlet form associated with it. For u∈D （ε）, u has a quasicontinuous version μz and μ（Xt ） has Fukushima＇s decomposition ：μ（Xt ） -μ（X0） = M^u ＋ Nt^u, where Mt^u is the martingale part and Nt^u is the zero energy part. In this paper we study the generalized Feynman-Kac semigroup Tf（x） = Ex^Nt^wf（Xt ）] for f∈（R^d ） 1 When μ〈u〉 which is the energy measure of u belongs to Hardy class with the constant 0 〈δμ〈u〉 〈1/2, we prove that （Tt） t〉0 is strongly continuous semigroup and identify the quadratic form associated with it.