Probabilistic setting of information-based complexity
We study the probabilistic (\(\epsilon\),\(\delta)\)-complexity for linear problems equipped with Gaussian measures. The probabilistic (\(\epsilon\),\(\delta)\)-complexity, \(comp^{prob}(\epsilon,\delta)\), is understood as the minimal cost required to compute approximations with error at most \(\epsilon\) on a set of measure at least 1-\(\delta\). We find estimates of \(comp^{prob}(\epsilon,\delta)\) in terms of eigenvalues of the correlation operator of the Gaussian measure over elements which we want to approximate. In particular, we study the approximation and integration problems.
scientific article; zbMATH DE number 4020477