Stochastic Partial Differential Equation Averaging.

[Alexey]

Whether somebody knows what equally

<int(F*Fcomp)dx>.

Where F(x,t) is complex function: F=F1+i*F2, Fcomp=F*=F1-i*F2.

F satisfies to the next Shredinger like linereal stochastic partial differential equation:

 

i*h*Ft=-a*(Fxx-2*n*Fx/x+(n+1)*F/x/x)+U*F

 

int - sing of integral by dx,

Ft - first time derivative,

Ftt - second time derivative,

Fx - first dpase derivative,

Fxx - second spase derivative,

i - imaginary unity,

< > - sign of averaging on casual fluctuations U,

U - casual space - time, delta - correlated a white noise,

a, h, n – are consts. ( If it matters - there are interesting to me the cases n=1 and n=0,5)