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In this paper we propose and study a family of continuous wavelets on generaldomains, and a corresponding stochastic discretization that we call Monte Carlowavelets. First, using tools from the theory of reproducing kernel Hilbertspaces and associated integral operators, we define a family of continuouswavelets by spectral calculus. Then, we propose a stochastic discretizationbased on Monte Carlo estimates of integral operators. Using concentration ofmeasure results, we establish the convergence of such a discretization andderive convergence rates under natural regularity assumptions.

Monte Carlo wavelets: a randomized approach to frame discretization