Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together transformations linearize compound Poisson processes. Furthermore, introduce stochastic integrating factor to solve linear equations. Extended Cox–Ingersoll–Ross, Brennan–Schwartz and Epstein be linearizable their explicit so...

We study and compare the decoherent histories approach, the environmentinduced decoherence and the localization properties of the solutions to the stochastic Schrödinger equation in quantum jump simulation and quantum state diffusion approaches, for a quantum two-level system model. We show, in particular, that there is a close connection between the decoherent histories and the quantum jump si...