totally_lost
May3-11, 06:00 AM
Dear all,
I have a PDF in independent variables q, \mu and h, all depending on x and y. I wish to check whether or not this PDF converges, which means checking that the normalisation constant converges in the limits -\infty and +\infty of the above mentioned variables q, \mu and h. The integral is given by
C^{-1} = \int dx dy \int\int\int dq dh d\mu h3 e-1/2\beta(g h2+h(k x \nablaInvLap(h q - f) + \nablaInvLap\mu)2) - h \sum \alphaj qj .
Note that q = q(x,y), h = h(x,y) and \mu = \mu(x,y), k = (0, 0, 1) and InvLap is the inverse laplacian operator. Beta and alpha_j are lagrange multipliers which may still be scaled freely. The sum runs from j=0 to j= K < infinity.
Any ideas on how to tackle this problem in terms of proving convergence are welcome.
I have a PDF in independent variables q, \mu and h, all depending on x and y. I wish to check whether or not this PDF converges, which means checking that the normalisation constant converges in the limits -\infty and +\infty of the above mentioned variables q, \mu and h. The integral is given by
C^{-1} = \int dx dy \int\int\int dq dh d\mu h3 e-1/2\beta(g h2+h(k x \nablaInvLap(h q - f) + \nablaInvLap\mu)2) - h \sum \alphaj qj .
Note that q = q(x,y), h = h(x,y) and \mu = \mu(x,y), k = (0, 0, 1) and InvLap is the inverse laplacian operator. Beta and alpha_j are lagrange multipliers which may still be scaled freely. The sum runs from j=0 to j= K < infinity.
Any ideas on how to tackle this problem in terms of proving convergence are welcome.