Affine Diffusion Processes: Theory and Applications

Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...

A Statistical Study of two Diffusion Processes on Torus and Their Applications

Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...

Polynomial processes and their applications to mathematical finance

We introduce a class of Markov stochastic processes called mpolynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains affine processes, Feller processes with quadratic squared diffusion coefficient, as well as Lévy-driven SDEs with affine vector fields. Thus, many popular models such as the classical Black-Sc...

application of affine gray-box neural models for nonlinear control of chemical processes

Face Recognition using an Affine Sparse Coding approach

Sparse coding is an unsupervised method which learns a set of over-complete bases to represent data such as image and video. Sparse coding has increasing attraction for image classification applications in recent years. But in the cases where we have some similar images from different classes, such as face recognition applications, different images may be classified into the same class, and hen...