Local Time Rough Path for Lévy Processes
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چکیده
In this paper, we will prove that the local time of a Lévy process is a rough path of roughness p a.s. for any 2 < p < 3 under some condition for the Lévy measure. This is a new class of rough path processes. Then for any function g of finite q-variation (1 ≤ q < 3), we establish the integral ∫∞ −∞ g(x)d L x t as a Young integral when 1 ≤ q < 2 and a Lyons’ rough path integral when 2 ≤ q < 3. We therefore apply these path integrals to extend the Tanaka-Meyer formula for a continuous function f if f ′ − exists and is of finite q-variation when 1 ≤ q < 3, for both continuous semi-martingales and a class of Lévy processes.
منابع مشابه
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تاریخ انتشار 2010