Probability density function is a statistical expression defining the likelihood of a series of outcomes for a continuous variable, such as a stock or ETF return.

A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates ...

We prove that for a diffusion process the first-passage-time p.d.f. through a continuous-time function with bounded derivative satisfies a Volterra integral equation of the second kind whose kernel ...