GARCH Model Applications. Comparison of Stationary Solutions of Stochastic Difference and Differential Equations

Main results for stochastic differential equations apply to their stationary solutions. For obvious reasons underlying processes are simulated with stochastic difference equations. Such equations also have stationary solutions that depend on the time step h. In the current paper relation between statistical features of stationary solutions of stochastic difference and differential equations are investigated. Moreover, possible approaches to the choice of time step h are discussed