We analyze the problem of recovering the pricing kernel and real probability distribution from observed option prices, when the state variable is an unbounded diffusion process. We derive necessary and sufficient conditions for recovery. In the general case, these conditions depend on the...

We investigate the joint distribution and the multivariate survival functions for the maxima of an Ornstein-Uhlenbeck (OU) process in consecutive time-intervals. A PDE method, alongside an eigenfunction expansion, is adopted with which we first calculate the distribution and the survival...

Motivated by path-integral numerical solutions of diffusion processes, PATHINT, we present a new tree algorithm, PATHTREE, which permits extremely fast accurate computation of probability distributions of a large class of general nonlinear diffusion processes

A class of measure-valued branching diffusions with interactive immigration is constructed by solving a stochastic integral equation with Poisson process based on a system of excursion laws of a Dawson-Watanabe superprocess, extending the results of Pitman and Yor (1982) and Shiga (1990)

How and to what extent will new activities spread through social ties? Here, we develop a more sophisticated framework than the standard mean-field approach to describe the diffusion dynamics of multiple activities on complex networks. We show that the diffusion of multiple activities follows a...