All Questions

I'd like to compute the derivative of an expected value w.r.t one of the parameters that define the mean of a Gaussian: $ Z=\int \mathcal{N}(x;\mu,\Sigma)f(x) \, dx $, then $ \frac{dZ}{dK}=\text{??}$ ...

I wonder if it is possible to solve analytically the following equation $$ \dot{\alpha}_t = -\frac{2}{m} \alpha^2_t + \frac{1}{2m} (\alpha_t - \alpha_t^*)^2 $$ Where $\alpha_t$ is a complex function, $...

Let $I(f)$ be an endomorphism of the smooth functions with zero value in zero such that: $$\ln[1+I(f)]=I\left(\frac{f}{1+I(f)}\right). $$ Then, does it exist $g$ smooth such that: $$I(f)(x)=\int_0^x f(...