Show that if X is a Bessel process of order 2, then the scale function is given by s(x) = log x, Y t = s(X t ) satisfies dY t = e −Yt dW t , and the speed measure is   Suppose X is a regular diffusion...

Show that if X is a Bessel process of order 2, then the scale function is given by s(x) = log x,

Y_t
= s(X_t) satisfies dY_t
= e^−Yt
dW_t, and the speed measure is

Suppose X is a regular diffusion whose state space is R. Prove that X is on natural scale if and only if

whenever a <>