Cauchyprocesser
Cauchyprocesser is commonly referred to in the context of probability theory as a stochastic process whose finite‐dimensional distributions are multivariate Cauchy. The process is a type of Lévy process, meaning it has stationary and independent increments, and it can be viewed as a continuous‐time analogue of the discrete Cauchy random walk. The one‐dimensional margins of the process at any fixed time are distributed according to the Cauchy distribution, characterized by a location parameter and a scale parameter that controls the heavy tails.
Although the process is self‐similar and stable, it does not possess finite moments beyond the first. This
Variants of the Cauchyprocesser can be constructed by mixing the Cauchy distribution with other Lévy process