Given a Stochastic differential equation $dN_t=\sqrt{2\mu N}dW_t$ starting with a deterministic initial value $N_O$.
How can I show that $E[\sup_{0 \le t \le T} N_t^2]<\infty$ for all $T>0$? I know that there exists a unique strong non-negative solution to the SDE and that its solution has a non-central chi-squared conditional distribution. How can I bound $E[\sup_{0 \le t \le T} N_t^2]$ by above given a T and do this for every $T>0$. Any hints would be appreciated