Local Time as a Rough Path
نویسندگان
چکیده
In this paper, we prove that a semimartingale local time is a rough path of roughness p for any p ∈ [2, 3) and establish the integral ∫∞ −∞ g(x)dLt(x) for any finite q-variation function g (2 ≤ q < 3) using Lyons’ rough path integration theory. We therefore obtain the Meyer-Tanaka’s formula for continuous function f if ∇−f exists and is of finite q-variation when 2 ≤ q < 3. The case when 1 ≤ q < 2 was established in [1] using Young integral.
منابع مشابه
Local Time Rough Path for Lévy Processes
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. W...
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