caa a22 4500 475839382 CHVBK 20180406123857.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1010734611017 doi (NATIONALLICENCE)springer-10.1023/A:1010734611017 Donsker's Delta Function of Lévy Process [Elektronische Daten] [Yuh-Jia Lee, Hsin-Hung Shih] Let X={X(t):t∈R} be a Lévy process and β a non-decreasing, right continuous, bounded function with β(−∞)=0 (((1+u 2)/u 2)dβ(u) is the Lévy measure). In this paper we define the Donsker delta function δ(X(t)−a), t>0 and a∈R, as a generalized Lévy functional under the condition that β(0)−β(0−)>0. This leads us to define F(X(t)) for any tempered distribution F, and as an application, we derive an Itô formula for F(X(t)) when β has jumps at 0 and 1. Kluwer Academic Publishers, 2000 white noise nationallicence Lévy process nationallicence Donsker's delta function nationallicence Lee Yuh-Jia Department of Mathematics, National Cheng Kung University, 70101, Tainan, Taiwan R.O.C aut Shih Hsin-Hung Department of Mathematics, National Cheng Kung University, 70101, Tainan, Taiwan R.O.C aut Acta Applicandae Mathematica Kluwer Academic Publishers 63/1-3(2000-09-01), 219-231 0167-8019 63:1-3<219 2000 63 10440 https://doi.org/10.1023/A:1010734611017 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1010734611017 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lee Yuh-Jia Department of Mathematics, National Cheng Kung University, 70101, Tainan, Taiwan R.O.C aut NATIONALLICENCE 700 1- Shih Hsin-Hung Department of Mathematics, National Cheng Kung University, 70101, Tainan, Taiwan R.O.C aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 63/1-3(2000-09-01), 219-231 0167-8019 63:1-3<219 2000 63 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer