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- W1922440261 abstract "In this paper, we will prove that the local time of a Levy process is of finite $p$-variation in the space variable in the classical sense, a.s. for any $p>2$, $tgeq 0$, if the Levy measure satisfies $int_{Rsetminus {0}}(|y|^{3over 2}wedge 1)n(dy)<infty$, and is a rough path of roughness $p$ a.s. for any $2<p<3$ under a slightly stronger condition for the Levy measure. Then for any function $g$ of finite $q$-variation ($1leq q <3$), we establish the integral $int_{-infty}^{infty}g(x)dL_t^x$ as a Young integral when $1leq q<2$ and a Lyons' rough path integral when $2leq q<3$. We therefore apply these path integrals to extend the Tanaka-Meyer formula for a continuous function $f$ if $nabla ^-f$ exists and is of finite $q$-variation when $1leq q<3$, for both continuous semi-martingales and a class of Levy processes." @default.
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- W1922440261 date "2008-11-13" @default.
- W1922440261 modified "2023-09-27" @default.
- W1922440261 title "Variation and Rough Path Properties of Local Times of L'evy Processes" @default.
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