No. 1011

Title:

Higher Order Local Linearization Methods for Solving Stochastic Differential Equations with Additive Noise

Author(s):

De la Cruz H. (Granma University);
Biscay R.J. (Institute of Cybernetics, Mathematics and Physics);
Carbonell F. (Institute of Cybernetics, Mathematics and Physics);
Ozaki T. (the Institute of Statistics Mathematics);
Jimenez J.C. (Institute of Cybernetics, Mathematics and Physics)

Key words:

Local Linearization; stochastic differential equations; numerical solution; stability.

Abstract:

A new class of methods for solving stochastic differential equations (SDEs) with additive noise is introduced. This is based on the addition, at each time step, of a suitable correction term to the LL approximate solution of the ordinary differential equation determined by the drift part of the original equation. This correction is computed by solving an auxiliary SDE, for which any extand numerical integrator can be applied. In particular, the use of (explicit) Taylor and Runge Kutta methods for this purpose yields, respectively, what we call the Local Linearization-Taylor (LLT) and Local Linearization-Runge Kutta (LLRK) methods. They retain the stability of the LL method and permit to achieve higher order of convergence. Their feasibility and performance are further illustrated through computer simulations.