the stochastic (Ito) differential equation dX1 = a X2 dt dX2 = -a X1 dt implies d(X1^2 + X2^2) = a^2 (X1^2 + X2^2) dt
dX1 = a X2 dt dX2 = -a X1 dt
implies
d(X1^2 + X2^2) = a^2 (X1^2 + X2^2) dt
dX1 = X2 (a dt + s dz1) dX2 = X1(- a dt + s dz2) implies d(X1^2 + X2^2) = a^2 s^2 (X1^2 + X2^2) dt + X1 X2(s1 dz1 + s2 dz2)
d(X1^2 + X2^2) = a^2 s^2 (X1^2 + X2^2) dt + X1 X2(s1 dz1 + s2 dz2)
