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-intersectionNature: Original
Retrieve article from Numdam
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 sheetNature: Original Retrieve article from Numdam
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 Retrieve article from Numdam
XXXIV: 05, 171-184, LNM 1729 (2000)
KASPI, Haya;
ROSEN, Jay S.
$p$-variation for families of local times on lines Retrieve article from Numdam
XXXVIII: 18, 263-281, LNM 1857 (2005)
ROSEN, Jay
Derivatives of self-intersection local times
XLIII: 03, 95-104, LNM 2006 (2011)
ROSEN, Jay
A stochastic calculus proof of the CLT for the $L^{2}$ modulus of continuity of local time (
Theory of Brownian motion)
Keywords: Central Limit Theorem,
Moduli of continuity,
Local times,
Brownian motionNature: Original
XLVII: 16, 299-320, LNM 2137 (2015)
FITZSIMMONS, Pat;
LE JAN, Yves;
ROSEN, Jay
Loop Measures Without Transition ProbabilitiesNature: Original
