Self-intersection local times, occupation fields, and stochastic integrals
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 X = (Xt,Ft)t≥0 be a continuous local martingale with quadratic variation process 〈X〉 and X0 = 0. Define iterated stochastic integrals In(X) = (In(t, X),Ft) (n ≥ 0), inductively by
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Sufficient conditions are obtained for the continuity of renormalized self-intersection local times for the multiple intersections of a large class of strongly symmetric Lévy processes in Rm, m = 1, 2. In R2 these include Brownian motion and stable processes of index greater than 3/2, as well as many processes in their domains of attraction. In R1 these include stable processes of index 3/4 < β...
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In this paper we apply Clark-Ocone formula to deduce an explicit integral representation for the renormalized self-intersection local time of the d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). As a consequence, we derive the existence of some exponential moments for this random variable.
متن کاملLarge deviations for self-intersection local times in subcritical dimensions
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: Advances in Mathematics
سال: 1987
ISSN: 0001-8708
DOI: 10.1016/0001-8708(87)90024-7