Asymptotic depth of Ext modules over complete intersection rings

Let $(A,mathfrak{m})$ be a local complete intersection ring and let $I$ be an ideal in $A$. Let $M, N$ be finitely generated $A$-modules. Then for $l = 0,1$, the values $depth Ext^{2i+l}_A(M, N/I^nN)$ become independent of $i, n$ for $i,n gg 0$. We also show that if $mathfrak{p}$ is a prime ideal in $A$ then the $j^{th}$ Bass numbers $mu_jbig(mathfrak{p}, Ext^{2i+l}_A(M,N/{I^nN})big)$ has polynomial growth in $(n,i)$ with rational coefficients for all sufficiently large $(n,i)$.