Recent content by mathy_girl

Whoops.. I just figured that there are two small mistakes in my first post, I would like to have the Inverse Fourier Transform of: \frac{\alpha^2}{2\pi}\exp\left(-\frac{1}{2} \alpha^2 C^2(K) \tau \omega^2\right) Here, note that \alpha is squared, and a minus sign is added in the argument of...

Hi all, I'm having a bit trouble computing the Inverse Fourier Transform of the following: \frac{\alpha}{2\pi}\exp\left(\frac{1}{2} \alpha^2 C^2(K) \tau \omega^2\right) Here, C^2(K), \alpha and \tau can be assumed to be constant. Hence, we have an integral with respect to \omega. Who...

Thanks for your explanation, I already didn't believe it would be that simple. In my case A and B are undetermined constants, so the solution in case the relation B = A^2 holds, cannot be used. I'll take a look at those Parabolic Cylinder Functions :-).

Then why does Maple give me such complicated solutions? Some Whittaker M function..? I don't really get it...

Nope, I didn't..

I forgot to say, the problem is on an infinite domain, -\infty < s < \infty. Can we still use this expansion in a series like you do?

Can anyone help me to solve the following second order linear 'ODE' for V(x,s,t): \frac{\partial^2 V(x,s,t)}{\partial s^2} = g(s) V(x,s,t) where g(s)=\frac{a^2}{B^4}+\frac{s^2 w^2}{B^2}. Here, a, b and w are (real) constants.

I'll try a Fourier transform on the original problem.. maybe that will help

That's always possible, but the assignment here is to do it analytically... Tomorrow I'll ask my supervisor if he thinks there's another way to solve this analytically.

Sorry, that's my mistake.. think it's a copy-paste error. I corrected it in the previous message.

Using perturbation theory, I'm trying to solve the following problem \frac{\partial P}{\partial \tau} = \frac{1}{2}\varepsilon^2 \alpha^2 \frac{\partial^2 P}{\partial f^2} + \rho \varepsilon^2 \nu \alpha^2 \frac{\partial^2 P}{\partial f \partial \alpha} + \frac{1}{2}\varepsilon^2 \nu^2...

Let me show you the complete problem then. Maybe that will make things a bit more clear. In the attachment you can find a part (scrap version of a chapter) of my report so far. Here I describe the problem completely. It's an application of perturbation methods on a financial model. Section...

I ment to say that p is defined as the (transition) probability of t going to T, f going to F and a going to A. Multiplying with increments dA and dF is because p itself is a probability distribution, which has to be integrated (it does not have a value in a point). Does this make it a bit...

I know, that's exactly what I've been doing. By applying this asymptotic theory (using the method of asymptotic expansions to solve a singular perturbation problem) I got to the problem I stated here... So applying it twice would be a bit strange, wouldn't it? About the books: Holmes indeed...

I hope some of you know something about transition density functions. I'm wondering if there are some nice properties I can use... Suppose p is a transition density function, defined as follows: p(t,f,a|T,F,A) dF dA := Prob(F<f<F+dF, A<a<A+dA | F(t)=f, A(t)=a). My question: what...