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I'm concerned with the following SDE: $$d Y_t= v \,dt + \sqrt {|Y_t|} \,d W_t$$ with $Y_0=-a$, $v>0$ being a constant, $a>0$ and $W_t$ as standard Brownian Motion. Do you have hints how to solve the SDE? Furthermore, I am interested in results (like density or moments) about the first hitting time of $a$ by the corresponding stochastic process.

Thanks a lot!

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    How about $v$ , is it a constant ? function ? – 2017-01-13
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    This is pretty close to the Cox-Ingersoll-Ross model for which the density and moments can be solved closed form (it also seems that your process stays always positive after it has reached a positive value). You could check if derivations for the CIR extend to your case somehow. – 2017-01-15

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