Malliavin calculus for stochastic differential equations driven by subordinated Brownian motions
Malliavin calculus for stochastic differential equations driven by subordinated Brownian motions
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DOI：
10.1215/0023608x-2010-003
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发表时间：
2010-09
影响因子：
0.6
通讯作者：
S. Kusuoka
中科院分区：
文献类型：
--
作者：
S. Kusuoka
Malliavin演算适用于由确定性时变布朗运动驱动的稳定过程的泛函，以及条件概率密度的存在性和正则性继承的条件，从而得到由从属布朗运动驱动的subordination.WeprepareMalliavincalculusforstochasticdifferentialequationsdriven。在[4]中也考虑了类似的问题。在本文中，我们考虑更一般的情况。我们还考虑了由旋转不变稳定过程驱动的方程。我们证明了当方程由一个旋转不变的稳定过程驱动时，方程的椭圆性意味着解的密度的存在性，并且证明了当方程由一个旋转不变的稳定过程驱动时，CoEffi元的正则性蕴含着密度的正则性。
Malliavin calculus is applicable to functionals of stable processes by using subordination.WeprepareMalliavincalculusforstochasticdifferentialequationsdriven by Brownian motions with deterministic time change, and the conditions that the existence and the regularity of the densities inherit from those of the densities of conditional probabilities.Byusingthese,weproveregularitypropertiesofthesolutionsofequations driven by subordinated Brownian motions. In [4] a similar problem is considered. In this article we consider more general cases. We also consider equations driven by rotation-invariant stableprocesses. Weprove that theellipticityof theequations impliesthe existence of the density of the solution, and we also prove that the regularity of the coefficients implies the regularity of the densities in the case when the equations are driven by one rotation-invariant stable process.