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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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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 motion

Nature: Original

XLVII: 16, 299-320, LNM 2137 (2015)

**FITZSIMMONS, Pat**; **LE JAN, Yves**; **ROSEN, Jay**

Loop Measures Without Transition Probabilities

Nature: Original

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

Comment: Closely related to 2036. A general reference is Le Gall,

Keywords: Local times, Self-intersection

Nature: Original

Retrieve article from Numdam

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

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

Nature: Original

Retrieve article from Numdam

XXVIII: 08, 102-109, LNM 1583 (1994)

Exact rates of convergence to the local times of symmetric Lévy processes

Retrieve article from Numdam

XXXIV: 05, 171-184, LNM 1729 (2000)

$p$-variation for families of local times on lines

Retrieve article from Numdam

XXXVIII: 18, 263-281, LNM 1857 (2005)

Derivatives of self-intersection local times

XLIII: 03, 95-104, LNM 2006 (2011)

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 motion

Nature: Original

XLVII: 16, 299-320, LNM 2137 (2015)

Loop Measures Without Transition Probabilities

Nature: Original