Nakajima, Tadashi The continuity of distribution-valued additive functionals for \(H_1^\beta\). (English) Zbl 1202.60127 Tokyo J. Math. 33, No. 1, 183-194 (2010). Summary: In [J. Math. Kyoto Univ. 40, No. 2, 293–314 (2000; Zbl 0981.60076) and J. Math. Kyoto Univ. 42, No. 3, 443–463 (2002; Zbl 1033.60082)], we discuss the existence and the \((a,t)\)-joint continuity of the distribution-valued additive functional \(A_T(a:t,\omega) = \int^t_0 T(X_s-a)\) for \(T \in H^{\beta}_p\) except for the case of the \((a,t)\)-joint continuity with \(p=1\). In this paper, we discuss the \((a,t)\)-joint continuity of the distribution-valued additive functional \(A_T(a:t,\omega)\) for \(T \in H^{\beta}_1\). MSC: 60J55 Local time and additive functionals Keywords:continuity; distribution-valued additive functional Citations:Zbl 0981.60076; Zbl 1033.60082 PDFBibTeX XMLCite \textit{T. Nakajima}, Tokyo J. Math. 33, No. 1, 183--194 (2010; Zbl 1202.60127) Full Text: DOI References: [1] T. Nakajima, A certain class of distribution-valued additive functionals I -for the case of Brownian motion, J. Math. Kyoto Univ., 40 , No. 2 (2000), 293-314. · Zbl 0981.60076 [2] T. Nakajima, A certain class of distribution-valued additive functionals II -for the case of stable process, J. Math. Kyoto Univ., 42 , No. 3 (2002), 443-463. · Zbl 1033.60082 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.