Theoretical aspects

Our team deals with the design of methods that:

1. define and study various relevant measures of local regularity,
2. allow to build stochastic models versatile enough to mimic the rapid variations of different kinds of regularities observed in real phenomena,
3. allow to estimate as precisely and rapidly as possible these regularities.

• Tools for measuring the (local) regularity

• Regularization dimension
• Stochastic 2-microlocal analysis
• Multifractal analysis

• Stochastic models with prescribed regularity

• Multifractional brownian motion
• Self-regulating processes
• Multistable processes
• Tempered multistable processes
• Multiparameter processes
• Statistics
• Machine learning