Lévy white noise measures on infinite-dimensional spaces: Existence and characterization of the measurable support |
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| Authors: | Yuh-Jia Lee Hsin-Hung Shih |
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| Institution: | a Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan
b Department of Accounting and Information, Kun Shan University, Tainan 710, Taiwan |
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| Abstract: | It is shown that a Lévy white noise measure Λ always exists as a Borel measure on the dual K′ of the space K of C∞ functions on R with compact support. Then a characterization theorem that ensures that the measurable support of Λ is contained in S′ is proved. In the course of the proofs, a representation of the Lévy process as a function on K′ is obtained and stochastic Lévy integrals are studied. |
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| Keywords: | Lé vy stochastic processes White noise measure Nuclear space |
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