Wong-Zakai Method Applications for Explicitly Solvable Stochastic Differential Equations
Süleyman Şengül *
Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey.
Mehmet Merdan
Department of Mathematical Engineering, Gumushane University, Gumushane, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this study, three Ito stochastic differential equations with multiplicative noise are investigated with Wong-Zakai method. The stochastic differential equations are also analyzed by Euler-Maruyama, Milstein and Runge Kutta stochastic approximation methods. The relative errors of these three methods are compared and the performance of Wong-Zakai method is shown alongside numerical results.
Keywords: Wong-Zakai method, stochastic differential equations, Euler method, Milstein method.