Sensitivity Analysis of the Expected Accumulated Reward Using Uniformization and IRK3 Methods

Abstract

This paper deals with the sensitivityc omputation of the expected accumulated reward of stiff Markov Models. Generally, we are faced with the problem of computation time, especiallywh en the Markov process is stiff. We consider the standard uniformization method for which we propose a new error bound. Because the time complexityo f this method becomes large when the stiffness increases, we then suggest an ordinary differential equations method, the third order implicit Runge-Kutta method. After providing a new way of writing the system of equations to be solved, we applythi s method with a stepsize choice different from the classical one in order to accelerate the algorithm execution. Finally, we compare the time complexity of both of the methods on a numerical example.