stochastic differential equation

Commodity price returns – especially those for fertilizers – are known to exhibit non-Gaussian features, time-varying behavior, and structural heterogeneity.  Simple models with constant parameters have a tendency to overlook such empirical attributes.  In this article, we propose a class of stochastic models designed to reflect the non-homogeneous (time-dependent) nature and heavy-tailed distributions of fertilizer price dynamics.  Our model extends the simple Ornstein–Uhlenbeck process by incorporating time-varying drift and diffusion terms.  Precisely, the long-run e

A Fokker–Plank equation of multiple variables corresponding to a system of SDE is considered.  Solution for transition probability density is written in a form of path integral.  It is shown that the proposed path integral brings a known result received by a different approach for Heston model. Differences of results based on path integral given in a number of papers were also pointed out.