For what values of a is this process a well defined Ito integral

Question

So the question is

For what values of a$\in$ $\mathbb{R}$ is the process

$$Y_{a}(t)=\int_{0}^{t}(t-s)^{a}dB(s) $$

Well defined as an Ito integral.

By well defined does it mean finite a.s? would it help to look at its expectoration or variance.