Spectral Density for Third Order Cumulants under Strong Mixing Conditions

If X:={Xv: v[set membership, variant]d} is a strictly stationary random field, with X0 bounded and expressible as a sum of indicator functions satisfying certain conditions, if the mixing coefficient [alpha](s) is summable over d (that, is, [summation operator]m md-1[alpha](m)<[infinity]), and if a mixing condition involving three sets is satisfied, then the third order cumulant Cum(Xa, Xb, Xc) of X has a continuous spectral density. We do not begin with the assumption that the cumulants are absolutely summable.