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4 matches found
XX: 33, 515-531, LNM 1204 (1986)
ROSEN, Jay S.
A renormalized local time for multiple intersections of planar Brownian motion (Brownian motion)
Using Fourier techniques, the existence of a renormalized local time for $n$-fold self-intersections of planar Brownian motion is obtained, thus extending the case $n=2$, obtained in the pioneering work of Varadhan (Appendix to Euclidean quantum field theory, by K.~Symanzik, in Local Quantum Theory, Academic Press, 1969)
Comment: Closely related to 2036. A general reference is Le Gall, École d'Été de Saint-Flour XX, Springer LNM 1527
Keywords: Local times, Self-intersection
Nature: Original
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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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XXVIII: 08, 102-109, LNM 1583 (1994)
MARCUS, Michael B.; ROSEN, Jay S.
Exact rates of convergence to the local times of symmetric Lévy processes
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XXXIV: 05, 171-184, LNM 1729 (2000)
KASPI, Haya; ROSEN, Jay S.
$p$-variation for families of local times on lines
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