Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion
Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion
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DOI：
10.1214/16-ejp4144
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发表时间：
2014-03
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影响因子：
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通讯作者：
Y. Inahama
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文献类型：
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作者：
Y. Inahama
研究了一类由Hurst参数为H（1/3 < H <= 1/2）的分数布朗粗糙路驱动的粗糙路理论意义下的随机微分方程.在这种情况下，在固定时间的解的规律具有核心，即，关于勒贝格测度的密度函数。在本文中，我们证明了一个短时间的非对角渐近展开的核在温和的附加假设。我们的主要工具是Watanabe的分布Malliavin演算。
We study a stochastic differential equation in the sense of rough path theory driven by fractional Brownian rough path with Hurst parameter H (1/3 < H <= 1/2) under the ellipticity assumption at the starting point. In such a case, the law of the solution at a fixed time has a kernel, i.e., a density function with respect to Lebesgue measure. In this paper we prove a short time off-diagonal asymptotic expansion of the kernel under mild additional assumptions. Our main tool is Watanabe's distributional Malliavin calculus.