论文标题
多重分数Ornstein-Uhlenbeck过程
Multifractal Fractional Ornstein-Uhlenbeck Processes
论文作者
论文摘要
Ornstein-Uhlenbeck过程可以看作是有限变化和统计固定的粗糙随机步行的范式。此外，它被定义为马尔可夫随机动力学的独特解决方案，并具有与布朗运动之一相同的局部规律性。该过程的自然概括能够重现参数h的分数布朗运动的局部规律性，这是由分数Ornstein-uhlenbeck过程提供的。基于以前的工作，我们建议使用高斯乘法混乱在此图片中包含一些多重校正校正。上述过程称为多重分数Ornstein-Uhlenbeck过程，是一个统计固定的有限变化过程。它的基本动力是非马克维亚人，尽管没有期待和因果关系。数值方案和理论方法是基于正规化程序，该过程赋予了这种动态演化的含义，该过程独特的解决方案将其收敛于行为良好的随机过程。
The Ornstein-Uhlenbeck process can be seen as a paradigm of a finite-variance and statistically stationary rough random walk. Furthermore, it is defined as the unique solution of a Markovian stochastic dynamics and shares the same local regularity as the one of the Brownian motion. A natural generalization of this process able to reproduce the local regularity of a fractional Brownian motion of parameter H is provided by the fractional Ornstein-Uhlenbeck process. Based on previous works, we propose to include some Multifractal corrections to this picture using a Gaussian Multiplicative Chaos. The aforementioned process, called a Multifractal fractional Ornstein-Uhlenbeck process, is a statistically stationary finite-variance process. Its underlying dynamics is non-Markovian, although non-anticipating and causal. The numerical scheme and theoretical approach are based on a regularization procedure, that gives a meaning to this dynamical evolution, which unique solution converges towards a well-behaved stochastic process.
