Hilbert coefficients of ideals under perturbation of an ideal

Let (R, m) be a noetherian local ring, J an m-primary ideal of R andI = (f1, ..., fr) an ideal generated by a filter regular sequence f1, ..., fr of R. In thispaper, we will prove the preserve of Hilbert coefficients of R/I with respect to Junder J-adic perturbation of I, provided that J is a parameter ideal generated by ad-sequence of R/(f1, ..., fi) for i = 1, ..., r.