Hello all,I have been working with the CIR interest rate model where,dr(t) = alpha(mew-r(t))dt + sigma.sqrt(r(t))dWtand using the bond pricing PDE,(dF/dt)+0.5.r.(sigma^2)(d2F/dr2) + (alpha(mew-r)-lambda.r)(dF/dr)-rF = 0I have been trying to derive the Feller condition, (2.alpha.mew)/sigma^2 > 1Where F = Ar^gamma and solving for gamma.(dF/dt)=0 (dF/dr)=gamma.A.r^gamma-1(d2F/dr2)=gamma(gamma-1)Ar^gamma-2I have been really struggling to get the final result out after substituting the PDEs into the bond pricing PDE as I don't really know were to go from there.Any help would be hugely appreciated,Tim

Since no one has answered, here is my two cents.The purpose of the Feller condition is to answer the question:For what parameters is the boundary r = 0 reachable by the process r(t) in finite expected time?There is a well-developed technology for answering such questions for -any- time-homogenous 1D diffusion, using the so-called scale and speed measures. To learn about all that, read Karlin & Taylor's, "A Second Course in Stochastic Processes" regards,

well you put in your solution to the original PDE and get a quadratic in gamma. This has two possible solutions.1) gamma =0. This is always possible2) gamma =1-(2\alpha\mu)/(\sigma*\sigma) This is possible when 2\alpha\mu/(\sigma*\sigma) <1.To ensure only one solution is ever possible require gamma \ge 2\alpha\mu/(\sigma*\sigma).

Also given in Proposition 6.2.4 of Lamberton and Lapeyre's book