  In this paper we propose and study a family of continuous wavelets on general
domains, and a corresponding stochastic discretization that we call Monte Carlo
wavelets. First, using tools from the theory of reproducing kernel Hilbert
spaces and associated integral operators, we define a family of continuous
wavelets by spectral calculus. Then, we propose a stochastic discretization
based on Monte Carlo estimates of integral operators. Using concentration of
measure results, we establish the convergence of such a discretization and
derive convergence rates under natural regularity assumptions.
