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XXV: 33, 407-424, LNM 1485 (1991)

**ROSEN, Jay S.**

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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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

Keywords: Local times, Stable processes, Method of moments, Fractional Brownian motion, Brownian sheet

Nature: Original

Retrieve article from Numdam