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XXV: 33, 407-424, LNM 1485 (1991)
Second order limit laws for the local times of stable processes (Limit theorems)
Using the method of moments, a central limit theorem is established for the increments $L^x_t-L^0_t$ of the local times of a symmetric $\beta$-stable process ($\beta>1$). The limit law is that of a fractional Brownian sheet, with Hurst index $\beta-1$, time-changed via $L_t^0$ in its time variable
Comment: Another proof due to Eisenbaum 3120 uses Dynkin's isomorphism. Ray-Knight theorems for these local times can be found in Eisenbaum-Kaspi-Marcus-Rosen-Shi Ann. Prob. 28 (2000). A good reference on this subject is Marcus-Rosen, Markov Processes, Gaussian Processes, and Local Times, Cambridge University Press (2006)
Keywords: Local times, Stable processes, Method of moments, Fractional Brownian motion, Brownian sheet
Nature: Original
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