Section: New Results

Level–dependent time deformation of Gaussian processes

Participant : Valérie Monbet.

Many records in environmental science exhibit asymmetries. In this project, we introduce a time deformation to produce asymmetric path from a Gaussian process with symmetric path. A simple case is obtained by assuming that

with $\left\{Y_t\right\}$ a stationary Gaussian process. The function $f$ which controls the time deformation is increasing. The time–change function $\phi$ is such that the modified time increases quicker when the process is at high levels and thus that the crests of the modified process $\left\{Z_t\right\}$ are narrower than the ones of $\left\{Y_t\right\}$. The opposite holds true for the troughs. Inference tools are developed to estimate the function $f$.