Derivatives of Self-intersection Local Times
Derivatives of Self-intersection Local Times
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DOI：
10.1007/978-3-540-31449-3_18
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发表时间：
2005
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影响因子：
--
通讯作者：
J. Rosen
中科院分区：
文献类型：
--
作者：
J. Rosen
我们证明了布朗运动和对称稳定过程inr1的重归一化自交局部时间$ γ t (x) $$\gamma_t(x)$在空间变量上是可微的，并且$ γ ′ t (0) $$\gamma'_t(0)$可以表征为自然Dirichlet过程分解中零二次变分的连续过程。这个狄利克雷过程是随机施瓦兹分布的势。讨论了r1r2r2自交局部时间的分数阶导数的类似结果。
We show that the renormalized self-intersection local time $ γ t (x) $$\gamma_t(x)$ for both the Brownian motion and symmetric stable process inR1is differentiable in the spatial variable and that $ γ ′ t (0) $$\gamma'_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. Analogous results for fractional derivatives of self-intersection local times inR1andR2are also discussed.