## Owen (1980) A table of normal integrals

This is an artcle of my recent acquaintance. It is about various integrals involving the standard normal distribution $$\Phi(x)$$ and its derivative. Besides it is a handy reference, it is interesting to see how the author organize the hundreds of integrals in a manner that is easy to lookup. [more]

## A rough description of Radon-Nikodym derivative

Radon-Nikodym theorem suggests, in simplified terms, that if we have two measures $$\mu,\lambda$$ of the same space with $$\mu$$ absolutely continuous with respect to $$\lambda$$ and a function $$\phi$$ is $$\mu$$-integrable, then $$\int_A \phi d\mu = \int_A \phi \frac{d\mu}{d\lambda} d\lambda$$ which the term $$d\mu/d\lambda$$ is called the Radon-Nikodym derivative. [more]

## Martingale and local martingale

Martingale is a stochastic process with the martingale property. If we have $$X_t$$ as the stochastic process, the martingale property says that $$\mathbf{E}[X_t\mid\mathcal{F}_s] = X_s$$, for $$s\lt t$$. Closely related to this is the local martingale. However, the Wikipedia page does not have it clearly explained. Here is my narrative.... [more]