Strong approximation of continuous time stochastic processes

Stochastic Processes in Continuous Time

1 Basic Concepts 3 1.1 Notions of equivalence of stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Sample path properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Properties of filtrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Stopping times . . . . . . . . . . . . . . . . . ....

strong approximation for itô stochastic differential equations

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

Strong approximation of stochastic processes using random walks

Part II CONTINUOUS TIME STOCHASTIC PROCESSES

Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes

In a recent paper Baier, Haverkort, Hermanns and Katoen [BHHK00], analyzed a new way of model-checking formulas of a logic for continuoustime processes called Continuous Stochastic Logic (henceforth CSL) – against continuous-time Markov chains – henceforth CTMCs. One of the important results of that paper was the proof that if two CTMCs were bisimilar then they would satisfy exactly the same fo...