Approximation of continuous time stochastic processes by a local linearization method

Approximation of continuous time stochastic processes by a local linearization method

This paper investigates the rate of convergence of an alternative approximation method for stochastic differential equations. The rates of convergence of the one-step and multi-step approximation errors are proved to be O((∆t)2) and O(∆t) in the Lp sense respectively, where ∆t is discrete time interval. The rate of convergence of the one-step approximation error is improved as compared with met...

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 . . . . . . . . . . . . . . . . . ....

Analysis of stochastic fluid queues driven by local time processes

We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically singular with respect to the Lebesgue measure which in many applications...

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...