Recent content by jend23

Hi haruspex, I really appreciate the time and effort you are putting into help me but I think we're having trouble communicating. I *don't* need to find a solution to the differential equation - this was my mistake so you can ignore my first post and attempted solution which you seem to be...

Doing the same for the second order term, I get: $$ \frac{d^2}{d\sigma^2} (b^2.p) = 2b.p.\frac{d^2b}{d\sigma^2} + 4b.\frac{db}{d\sigma}.\frac{dp}{d\sigma} + 2p.(\frac{db}{d\sigma})^2 + b^2.\frac{d^2p}{d\sigma^2} $$ Which doesn't seem to help me show that the equation for ##p## satisfies the...

So, $$ \frac{\partial}{\partial\sigma} (ap) = a.\frac{\partial p}{\partial\sigma} + \frac{\partial a}{\partial\sigma}.p $$ Given the boundary conditions in the question ##p → 0## and ##\frac{\partial p}{\partial\sigma} → 0##, does this mean that: $$ \frac{\partial}{\partial\sigma} (ap) = a.0...

OK, but how does that help me show that the given equation for p satisfies the PDE? I'm honestly more lost now than I was at the beginning of the thread.

Hi, apparently that whole line of attack is not what the question is asking. I'm supposed to show that the equation given, satisfies the PDE.

OK, I'm back on this one. What you're suggesting seems to be more of a challenge than the derivation I computed. I'm having a complete mental block. Can somebody get me started? ## \frac{∂}{∂\sigma}(ap) = \frac{∂}{∂\sigma} (a \frac{A}{b^2}e^{\int\frac{2a}{b^2}d\sigma}) ## But the...

Hi Ray, thanks for the help again. The dummy variable point makes sense. On the topic of "verification" vs. "discovery" are you saying that the problem isn't to solve the differential equation? (which I have now done, more or less - see below). If not, what exactly is it that I'm supposed...

Can anybody help? Still stuck on this one. It's really a differential equation problem...

Essentially, this looks like a differential equation problem but being rusty on differential equations I am a little stuck. Homework Statement Consider the following SDE d\sigma = a(\sigma,t)dt + b(\sigma,t)dW The Forward Equation (FKE) is given by \frac{\partial p}{\partial t} =...

Thanks for the pointer and after reviewing my notes a few more times, it has now become embarrassingly obvious. Much appreciated. So, we have dX = (\alpha - \beta X)dt + \delta dW \frac{∂Y}{∂t} = 0, \frac{∂Y}{∂X} = 2x, \frac{∂^2Y}{∂X^2} = 2 therefore, from (slightly different...

Hello, Homework Statement Given the process d\sqrt{z} = (\alpha - \beta\sqrt{z})dt + \delta dW \alpha, \beta and \delta are constants. Use Ito's Lemma to show that: dz = (\delta^2 + 2\alpha\sqrt{z} - 2\beta z)dt + 2\delta\sqrt{z}dW Homework Equations Itos Lemma: df =...