Optimal Bounds for the Variance of Self-Intersection Local Times
نویسندگان
چکیده
منابع مشابه
Derivatives of self-intersection local times
We show that the renormalized self-intersection local time γt(x) for both the Brownian motion and symmetric stable process in R is differentiable in the spatial variable and that γ′ t(0) can be characterized as the continuous process of zero quadratic variation in the decomposition of a natural Dirichlet process. This Dirichlet process is the potential of a random Schwartz distribution. Analogo...
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Let (Xt, t ≥ 0) be a simple symmetric random walk on Z and for any x ∈ Z, let lt(x) be its local time at site x. For any p > 1, we denote by It = ∑ x∈Zd lt(x) p the p-fold self-intersection local times (SILT). Becker and König [6] recently proved a large deviations principle for It for all p > 1 such that p(d − 2/p) < 2. We extend these results to a broader scale of deviations and to the whole ...
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ژورنال
عنوان ژورنال: International Journal of Stochastic Analysis
سال: 2016
ISSN: 2090-3332,2090-3340
DOI: 10.1155/2016/5370627