For a class of anisotropic integrodifferential operators $ℬ$ arising as semigroup generators of Markov processes, we present a sparse tensor product wavelet compression scheme for the Galerkin finite element discretization of the corresponding integrodifferential equations $ℬ$ u = f on [0,1]n with possibly large n. Under certain conditions on $ℬ$, the scheme is of essentially optimal and dimension independent complexity $𝒪$(h-1| log h |2(n-1)) without corrupting the convergence or smoothness requirements...