Please is there a way to solve lim as h approach infinity of||f_h(x)-f(x)||_HS (HS-Hilbert Schmidts norm) where f_h(x) is a regularized form of compensator f(x) in marked point process. I know in functions we can use some known theories and lemma's like fubini theorem, dominated convergence theorem to solve it but I am not sure of what I can do since I am working in marked point process environment. Should I use martingales or what. Please help if you can
I am thinking of martingales but do not know how to tackle it. Also I am thinking or using orthogonal identities like cosx and sinx to act of f_h(x) since we are working in HS (Hilbert-Schmidt norm) but I am stacked