Asymptotic behaviour of the solution to a certain PDE - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T19:20:53Z http://mathoverflow.net/feeds/question/72851 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72851/asymptotic-behaviour-of-the-solution-to-a-certain-pde Asymptotic behaviour of the solution to a certain PDE Epsilon 2011-08-13T22:57:35Z 2011-08-13T23:03:05Z <p>$\delta M=\beta(x-y)M_y+\mu x(y-1)M_x+\delta y$, where $M(x,y)=\sum_{n=0}^{\infty}{\sum_{k=0}^{\infty}{s_{n,k}x^ny^k}}$ is the generating function for a certain probability distribution ${s_{n,k}}$ (the exact formula for $s_{n,k}$ is unknown), and $\delta$, $\beta$, $\mu$ are all constants. </p> <p>The problem comes out of a probability model, and data show that the distribution should have a finite mean and divergent moment ($M_{xx}(1,1)=\infty$). My question is that is there any way to get the asymptotic of $M_{xx}(x,1)$ when $x\rightarrow 1^{-}$? (by asymptotic I mean something like $M_{xx}(x,1)\sim C(1-x)^{-\zeta}$)</p> <p>Thank you!</p>