Let X be of the form X t = t 0 b s dZ s + t 0 a s ds, t ≥ 0, where Z is a symmetric stable process of index α ∈ (1, 2) with Z 0 = 0. We obtain various L 2 -estimates for the process X. In particular, for m ∈ N, t ≥ 0, and any measurable, nonnegative function f we derive the inequality As an application of the obtained estimates, we prove the existence of solutions for the stochastic equation dX t = b(X t− )dZ t + a(X t )dt for any initial value x 0 ∈ R.