论文标题
低纤维化扩散过程的密度估计和短期渐近造成
Density estimates and short-time asymptotics for a hypoelliptic diffusion process
论文作者
论文摘要
我们研究一个$ n $微分方程的系统，每个方程都在尺寸$ d $中。只有第一个方程是由布朗运动强迫的，并且依赖性结构使得在局部弱的Hörmander条件下，噪声会传播到整个系统。我们证明了过渡密度（热核）及其衍生物的上限。然后，我们在适当的中央限制时间尺度上提供了密度的精确短期渐近造型。这两个结果都说明了各个组件中不同的非扩展量表。最后，我们提供了一个相关的本地波动率动力学的亚洲篮子选项的估值公式。
We study a system of $n$ differential equations, each in dimension $d$. Only the first equation is forced by a Brownian motion and the dependence structure is such that, under a local weak Hörmander condition, the noise propagates to the whole system. We prove upper bounds for the transition density (heat kernel) and its derivatives of any order. Then we give precise short-time asymptotics of the density at a suitable central limit time scale. Both these results account for the different non-diffusive scales of propagation in the various components. Finally, we provide a valuation formula for short-maturity at-the-money Asian basket options under correlated local volatility dynamics.
