I'm trying to find the distribution of a random variable ##T## supported on ##[t_1, t_2]## subject to ## \mathbb{E}[V(t', T)] = K, \forall t' \in [t_1, t_2]##. In integral form, this is : $$ \int_{t_1}^{t_2} V(t', t).f(t) \, dt = K,\forall t' \in [t_1, t_2], $$ which is just an exotic integral transform.(adsbygoogle = window.adsbygoogle || []).push({});

So if I can find the inverse transform, I'm done. But the function ##V## is ...not nice. It's nowhere differentiable for ##t < t'##, there's a jump at ##t = t'## and it's constant from then on.

So do you guys know of any methods to find the inverse to an integral transform with a nasty kernel like ##V##? Or can you see another way to solve these equations? I'd even be happy with numerical techniques.

Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I How to find the inverse of an integral transform?

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**