论文标题
多重过程：定义，属性和新示例
Multifractal processes: Definition, properties and new examples
论文作者
论文摘要
我们研究具有比例不变特性的随机过程，我们称之为多重分子过程。到目前为止已知的此类过程的例子并没有超出Mandelbrot的原始级联构造。我们通过概括自相似过程的定义来提供多重过程的新定义。我们建立了这些过程的一般属性，并展示了现有示例如何适合我们的设置。最后，我们定义了一个新的示例，灵感来自Lamperti Transformation的想法。也就是说，对于任何一对无限划分的分布和固定过程，都可以构建多重分子过程。
We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much beyond the original cascade construction of Mandelbrot. We provide a new definition of the multifractal process by generalizing the definition of the self-similar process. We establish general properties of these processes and show how existing examples fit into our setting. Finally, we define a new class of examples inspired by the idea of Lamperti transformation. Namely, for any pair of infinitely divisible distribution and a stationary process one can construct a multifractal process.
