most citedLarge deviations for renormalized self-intersection local times of stable processes

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math.PR2005★ 21 cited

Large deviations for renormalized self-intersection local times of stable processes

Richard Bass, Xia Chen, Jay Rosen

We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index β\in (2d/3,d]. We find a difference between the upper and low…

math.PR2005★ 28 cited

Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks

Xia Chen

Let α([0,1]^p) denote the intersection local time of p independent d-dimensional Brownian motions running up to the time 1. Under the conditions p(d-2)<d and d\ge 2, we prove lim_{…

math.PR2005★ 48 cited

Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm

Richard F. Bass, Xia Chen

If β_t is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee^{γβ_1} is finite or infinite in terms of the best constant of a Gagliardo-Ni…