Numerical analysis of the master equation.

A master equation approach to option pricing

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black–Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option price variable. The dynamics of the latter is constructed and formulated in terms of a master equation. The numerical efficiency of the approach is demonstrat...

Analysis of Goldbeter-Koshland Switch Using the Chemical Master Equation

The chemical master equation is considered as an accurate description of general chemical systems, and especially so for modeling gene regulatory networks and protein-protein interaction networks. This paper examines some “off-the-shelf” numerical approaches to solve the chemical master equation for the Goldbeter-Koshland switch on both sequential and parallel machines. The numerical results sh...

Numerical solution of fuzzy Hunter-Saxton equation by using Adomian decomposition and Homotopy analysis methods

In this paper, a fuzzy Hunter-Saxton equation is solved by using the Adomian'sdecomposition method (ADM) and homotopy analysis method (HAM). Theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. The existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. A numerical...

On Reduced Models for the Chemical Master Equation

Abstract. The chemical master equation plays a fundamental role for the understanding of gene regulatory networks and other discrete stochastic reaction systems. Solving this equation numerically, however, is usually extremely expensive or even impossible due to the huge size of the state space. Thus, the chemical master equationmust often be replaced by a reducedmodel which operates with a con...

Numerical Methods for the Chemical Master Equation

NUMERICAL SOLUTION OF BOUSSINESQ EQUATION USING MODIFIED ADOMIAN DECOMPOSITION AND HOMOTOPY ANALYSIS METHODS

In this paper, a Boussinesq equation is solved by using the Adomian's decomposition method, modified Adomian's decomposition method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods ...