# Monte Carlo methods for $L_q$ approximation on periodic Sobolev spaces with mixed smoothness

ASCW01 - Challenges in optimal recovery and hyperbolic cross approximation

In this talk we consider multivariate approximation of compact embeddings of periodic Sobolev spaces of dominating mixed smoothness into the $L_q,\ 2< q\leq \infty$ space by linear Monte Carlo methods that use arbitrary linear information. We construct linear Monte Carlo methods and obtain explicit-in-dimension upper estimates. These estimates catch up with the rate of convergence.

This talk is part of the Isaac Newton Institute Seminar Series series.