In this article, we derive a solution for a linear stochastic model on a complex time domain. In this type of models, the time domain can be any collection of points along the real number line, so these models are suitable for problems where events do not occur at evenly-spaced time intervals....

Although spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not always so for some non-stationary cases. Here, we establish a rigorous mathematical extension of the classic Fourier spectrum to the case in which there are AR roots in the unit circle,...

We study the existence of solutions to backward stochastic differential equations with drivers f(t,W,y,z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the existence of a unique solution (Y,Z) with bounded Z if...